Kinetic Simulation Algorithm Ontology
http://www.biomodels.net/kisao/
2.1
KiSAO
The Kinetic Simulation Algorithm Ontology (KiSAO) classifies algorithms available for the simulation of Systems Biology models.
This is a core version, which contains all but deprecated classes.
has characteristic
'has characteristic' links algorithms to the characteristics, they possess.
KISAO
is hybrid of
urn:miriam:doi:10.1093/bib/bbn050
KISAO
The basic idea of hybrid simulation methods is to combine the advantages of complementary simulation approaches: the whole system is subdivided into appropriate parts and different simulation methods operate on these parts at the same time.
'is hybrid of' is a relation between the complex simulation method and algorithms it applies to the different parts of the system.
is parameter of
'is parameter of' is an inverse of 'has parameter' and links parameters to the algorithms which use them.
KISAO
has parameter
'has parameter' links algorithms to the parameters they use.
KISAO
is characteristic of
'is characteristic of' is an inverse of 'has characteristic' and links characteristics to the algorithms which possess them.
KISAO
is similar to
2011-06-10
A relationship indicating that two entities are similar to each other.
AZ
KISAO
uses
2011-06-10
A relation between simulation algorithms indicating that one algorithm uses another one (for example, if the algorithm switches between several algorithms).
AZ
KISAO
is generalization of
2011-06-10
A relation between kinetic simulation algorithms, indicating that one is a generalization of another (e.g.if one extends another to suit systems with more general characteristics ).
AZ
KISAO
has type
Indicates the type of algorithm parameter value, such as, for example, xsd:double for 'absolute tolerance'.
KISAO
kinetic simulation algorithm
2008-05-26
true
Algorithm used to instantiate a simulation from a mathematical model, where the variable values evolve over time.
KISAO
dk
weighted stochastic simulation algorithm
24JAN2009
urn:miriam:pubmed:19045316
KISAO
NLN
The weighted Stochastic Simulation Algorithm manipulates the probabilities measure of biochemical systems by sampling, in order to increase the fraction of simulation runs exhibiting rare events.
weighted SSA
Gillespie first reaction algorithm
2007-11-09
urn:miriam:doi:10.1016/0021-9991(76)90041-3
Cain
Gillespie's first reaction method
KISAO
NLN
Stochastic simulation algorithm using the next-reaction density function, giving the probability that the next reaction will happen in a given time interval. To choose the next reaction to fire, the algorithm calculates a tentative reaction time for each reaction and then select the smallest.
multi-state agent-based simulation method
urn:miriam:pubmed:9628844
KISAO
Morton-Firth
StochSim
The agent-based simulation method instantiates each molecule as an individual software object. The interactions between those objects are determined by interaction probabilities according to experimental data. The probability is depended on the state the molecule is in at that specific time (molecules have multiple-state). Additionally, ''pseudo-molecules'' are introduced to the system in order to simulate unimolecular reactions. For simulation, continuous time is broken down into discrete, independent ''slices''. During each time slice one molecule is selected randomly, a second molecule or pseudo-molecule is selected afterwards (leading to either a unimolecular or a bimolecular reaction). The reaction will only take place if a produced random number exceeds the reaction probability calculated beforehand. In that case, the system is updated after that reaction.
CVODE
2007-11-30
citeulike:1832863
code value ordinary differential equation solver
urn:miriam:doi:10.1145/1089014.1089020
BioNetGen
JSim
KISAO
SBML-SAT
The CVODE is a package written in C that solves initial value problems for ODEs. It is capable for stiff and non-stiff systems and uses two different linear multi-step methods, namely the Adam-Moulton [urn:miriam:biomodels.kisao:KISAO_0000280] method and the backward differentiation formula [urn:miriam:biomodels.kisao:KISAO_0000288].
VCell
VODE
VODEPK
code value ordinary differential equation solver
dk
PVODE
urn:miriam:doi:10.1145/1089014.1089020
urn:miriam:doi:10.1177/109434209901300405
KISAO
PVODE is a general-purpose solver for ordinary differential equation (ODE) systems that implements methods for both stiff and nonstiff systems. [...] In the stiff case, PVODE uses a backward differentiation formula method [urn:miriam:biomodels.kisao:KISAO_0000288] combined with preconditioned GMRES [urn:miriam:biomodels.kisao:KISAO_0000253] iteration. Parallelism is achieved by distributing the ODE solution vector into user-specified segments and parallelizing a set of vector kernels accordingly. For PDE-based ODE systems, we provide a module that generates a band block-diagonal preconditioner for use with the GMRES [urn:miriam:biomodels.kisao:KISAO_0000253] iteration. PVODE is based on CVODE [urn:miriam:biomodels.kisao:KISAO_0000019].
parallel code value ordinary differential equation solver
StochSim nearest-neighbour algorithm
urn:miriam:pubmed:11395441
KISAO
Stochsim 1.2 and more recent versions
The nearest-neighbour algorithm allows for the representation of spatial information, by adding a two-dimensional lattice in the form of a probabilistic cellular automata. That way, nearest neighbour interactions do additionally influence reactions taking place in the systems. Reactions between entities are calculated using the agent-based simulation algorithm [urn:miriam:biomodels.kisao:KISAO_0000017].
Elf and Ehrenberg method
urn:miriam:doi:10.1049/sb:20045021
Elf algorithm
KISAO
MesoRD
NSM
SmartCell
Sub-volume stochastic reaction-diffusion method that is a combination of the Direct Method [urn:miriam:biomodels.kisao:KISAO_0000029] for sampling the time for a next reaction or diffusion event in each subvolume, with Gibson and Bruck's Next Reaction Method [urn:miriam:biomodels.kisao:KISAO_0000027], which is used to keep track of in which subvolume an event occurs next. The subvolumes are kept sorted in a queue, implemented as a binary tree, according to increasing time of the next event. When an event has occurred in the subvolume at the top of the queue, new event times need to be sampled only for one (the event is a chemical reaction) or two (the event is a diffusion jump) subvolume(s).
next-subvolume method
Gibson-Bruck next reaction algorithm
2007-11-10
urn:miriam:doi:10.1021/jp993732q
As with the first reaction method [urn:miriam:biomodels.kisao:KISAO_0000015], a putative reaction time is calculated for each reaction, and the reaction with the shortest reaction time will be realized. However, the unused calculated reaction times are not wasted. The set of reactions is organized in a priority queue to allow for the efficient search for the fastest reaction. In addition, by using a so-called dependency graph only those reaction times are recalculated in each step, that are dependent on the reaction, which has been realized.
Cain
E-Cell
Gibson and Bruck algorithm
Gibson-Bruck's next reaction algorithm
Gillespie-Gibson stochastic simulation algorithm
KISAO
SSA-GB
SmartCell
VCell
dk
next reaction method
slow-scale stochastic simulation algorithm
urn:miriam:pubmed:15638651
Attempt to overcome the problem of stiff systems by developing an ''approximate theory that allows one to stochastically advance the system in time by simulating the firings of only the slow reaction events''.
KISAO
slow-scale stochastic SSA
ssSSA
Gillespie direct algorithm
2007-11-10
urn:miriam:doi:10.1021/j100540a008
BetaWB
BioNetGen
ByoDyn
Cain
DM
Doob-Gillespie method
Gillespie's direct method
KISAO
SSA
Stochastic simulation algorithm using the next-reaction density function, giving the probability that the next reaction will happen in a given time interval. To choose the next reaction to fire, the algorithm directly and separately calculate the identity of the reaction and the time it will fire.
dk
iBioSim
stochastic simulation algorithm
Euler forward method
2007-11-10
urn:miriam:isbn:052143064X
KISAO
The Euler method is an explicit one-step method for the numerical integration of ODES with a given initial value. The calculation of the next integration step at time t+1 is based on the state of the system at time point t.
VCell
dk
explicit Euler method
iBioSim
Euler backward method
2007-11-02
urn:miriam:isbn:052143064X
KISAO
The Euler backward method is an implicit one-step method for the numerical integration of ODES with a given initial value. The next state of a system is calculated by solving an equation that considers both, the current state of the system and the later one.
dk
implicit Euler method
explicit fourth-order Runge-Kutta method
2007-11-12
urn:miriam:isbn:0-471-91046-5
ERK4
JSim
KISAO
RK4
Runge-Kutta method
The Runge-Kutta method is a method for the numerical integration of ODES with a given initial value. The calculation of the next integration step at time t+1 is based on the state of the system at time point t, plus the product of the size of the interval and an estimated slope. The slope is a weighted average of 4 single slope points (beginning of interval-midpoint-midpoint-end of interval).
VCell
dk
Rosenbrock method
2007-11-12
urn:miriam:doi:10.1093/comjnl/5.4.329
urn:miriam:isbn:052143064X
E-Cell
KISAO
Kaps-Rentrop method
Some general implicit processes are given for the solution of simultaneous first-order differential equations. These processes, which use successive substitution, are implicit analogues of the (explicit) Runge-Kutta processes. They require the solution in each time step of one or more set of simultaneous linear equations, usually of a special and simple form. Processes of any required order can be devised, and they can be made to have a wide margin of stability when applied to a linear problem.
dk
generalized fourth order Runge-Kutta method
sorting stochastic simulation algorithm
urn:miriam:doi:10.1016/j.compbiolchem.2005.10.007
In order to overcome the problem of high complexity of the Stochastic Simulation Algorithm [urn:miriam:biomodels.kisao:KISAO_0000029] when simulating large systems, the sorting direct method maintains a loosely sorted order of the reactions as the simulation executes.
KISAO
sorting SSA
sorting direct method
tau-leaping method
2008-07-08
urn:miriam:doi:10.1063/1.1378322
Approximate acceleration procedure of the Stochastic Simulation Algorithm [urn:miriam:biomodels.kisao:KISAO_0000029] that divides the time into subintervals and ''leaps'' from one to another, firing all the reaction events in each subinterval.
ByoDyn
Cain
KISAO
NLN
SmartCell
tauL
Poisson tau-leaping method
explicit tau-leaping method with basic pre-leap check
urn:miriam:doi:10.1063/1.1378322
ByoDyn
Explicit tau-leaping method with basic pre leap check.
KISAO
explicit tau-leaping
explicit tau-leaping method with basic preleap check
poisson tau-leaping
implicit tau-leaping method
2007-10-12
urn:miriam:doi:10.1063/1.1627296
Contrary to the explicit tau-leaping [urn:miriam:biomodels.kisao:KISAO_0000039 and urn:miriam:biomodels.kisao:KISAO_0000245 some urn:miriam:biomodels.kisao:KISAO_0000239] , the implicit tau-leaping allows for much larger time-steps when simulating stiff systems.
KISAO
dk
trapezoidal tau-leaping method
2007-10-16
citeulike:1755561
trapezoidal implicit tau-leaping method
Formula for accelerated discrete efficient stochastic simulation of chemically reacting system [which] has better accuracy and stiff stability properties than the explicit and implicit [urn:miriam:biomodels.kisao:KISAO_0000045] tau-leaping formulas for discrete stochastic systems, and it limits to the trapezoidal rule in the deterministic regime.
KISAO
dk
trapezoidal implicit tau-leaping method
adaptive explicit-implicit tau-leaping method
urn:miriam:doi:10.1063/1.2745299
KISAO
Modification of the original tau-selection strategy [urn:miriam:biomodels.kisao:KISAO_0000040], designed for explicit tau-leaping, is modified to apply to implicit tau-leaping, allowing for longer steps when the system is stiff. Further, an adaptive strategy is proposed that identifies stiffness and automatically chooses between the explicit and the (new) implicit tau-selection methods to achieve better efficiency.
Bortz-Kalos-Lebowitz algorithm
urn:miriam:doi:10.1016/0021-9991(75)90060-1
BKL
DMC
KISAO
KMC
The Bortz-Kalos-Lebowitz (or: kinetic Monte-Carlo-) method is a stochastic method for the simulation of time evolution of processes using (pseudo-)random numbers.
dynamic Monte Carlo
dynamic Monte Carlo method
kinetic Monte Carlo
kinetic Monte Carlo method
n-fold way
Smoluchowski equation based method
2007-10-29
true
urn:issn:0942-9352
KISAO
Methods based on the Smoluchowski equation.
dk
Brownian diffusion Smoluchowski method
urn:miriam:pubmed:16204833
In the Brownian diffusion Smoluchowski method, ''each molecule is treated as a point-like particle that diffuses freely in three-dimensional space. When a pair of reactive molecules collide, such as an enzyme and its substrate, a reaction occurs and the simulated reactants are replaced by products. [..] Analytic solutions are presented for some simulation parameters while others are calculated using look-up tables''. Supported chemical processes include molecular diffusion, treatment of surfaces, zeroth-order-, unimolecular-, and bimolecular reactions.
KISAO
Smoldyn
Greens function reaction dynamics
urn:miriam:doi:10.1063/1.2137716
GFRD
Green's function reaction dynamics
KISAO
Method that simulates biochemical networks on particle level. It considers both changes in time and space by ''exploiting both the exact solution of the Smoluchowski Equation to set up an event-driven algorithm'' which allows for large jumps in time when the considered particles are far away from each other [in space] and thus cannot react. GFRD combines the propagation of particles in space with the reactions taking place between them in one simulation step.
Runge-Kutta based method
2007-11-12
true
urn:miriam:isbn:0-471-91046-5
A method of numerically integrating ordinary differential equations, which uses a sampling of slopes through an interval and takes a weighted average to determine the right end point. This averaging gives a very accurate approximation.
ByoDyn
KISAO
dk
modified Euler method
deterministic cellular automata update algorithm
2007-11-30
urn:miriam:isbn:978-0252000232
A cellular automaton is a discrete model of a regular grid of cells with a finite number of dimensions. Each cell has a finite number of defined states. The automaton changes its state in a discrete manner, meaning that the state of a cell at time t is determined by a function of the states of its neighbours at time t - 1. These neighbours are a selection of cells relative to the specified cell. Famous examples for deterministic cellular automata are Conway's game of life or Wolfram's elementary cellular automata.
KISAO
dk
LSODE
2007-11-16
citeulike:1774586
urn:miriam:doi:10.1145/1218052.1218054
KISAO
LSODE solves stiff and nonstiff systems of the form dy/dt = f. In the stiff case, it treats the Jacobian matrix sf/dy as either a dense (full) or a banded matrix, and as either user-supplied or internally approximated by difference quotients. It uses Adams methods (predictor-corrector) [urn:miriam:biomodels.kisao:KISAO_0000364] in the nonstiff case, and Backward Differentiation Formula (BDF) methods (the Gear methods) [urn:miriam:biomodels.kisao:KISAO_0000288] in the stiff case.
Livermore solver for ordinary differential equations
dk
binomial tau-leaping method
2007-10-16
binomial tau-leap spatial stochastic simulation algorithm
urn:miriam:doi:10.1063/1.2771548
BtauL
Coarse grained modified version of the next subvolume method [urn:miriam:biomodels.kisao:KISAO_0000022] that allows the user to consider both diffusion and reaction events in relatively long simulation time spans as compared with the original method and other commonly used fully stochastic computational methods.
KISAO
binomial tau-leap spatial stochastic simulation algorithm
dk
Gillespie multi-particle method
urn:miriam:pubmed:16731694
Combination of the multiparticle method for diffusion [urn:miriam:biomodels.kisao:KISAO_0000334] and the SSA [urn:miriam:biomodels.kisao:KISAO_0000029].
GMP
Gillespie's multi-particle method
KISAO
particle-based spatial stochastic method
Stundzia and Lumsden method
urn:miriam:doi:10.1006/jcph.1996.0168
KISAO
RD SSA
Sub-volume stochastic reaction-diffusion method that using Green's function to link the bulk diffusion coefficient D in Fick's differential law to the corresponding transition rate probability for diffusion of a particle between finite volume elements. This generalized stochastic algorithm enables to numerically calculate the time evolution of a spatially inhomogeneous mixture of reaction-diffusion species in a finite volume. The time step is stochastic and is generated by a probability distribution determined by the intrinsic reaction kinetics and diffusion dynamics.
reaction-diffusion stochastic simulation algorithm
estimated midpoint tau-leaping method
urn:miriam:doi:10.1063/1.1378322
Estimated-Midpoint tau-Leap Method: For the selected leaping time tau which satisfies the Leap Condition, compute the expected state change lambda' = tau sumj( aj(x)vj ) during [t, t + tau). Then, with x' =x + [lambda'/2], generate for each j = 1,...,M a sample value kj of the Poisson random variable P(aj(x'), tau). Compute the actual state change, lambda = sumj( kjvj ), and effect the leap by replacing t by t + tau and x by x + lambda.
KISAO
explicit tau-leaping method with estimated-mid point technique
k-alpha leaping method
urn:miriam:doi:10.1063/1.1378322
Alternative to the tau-leaping [urn:miriam:biomodels.kisao:KISAO_0000039], where one leaps a fixed number of reaction-events.
KISAO
nonnegative Poisson tau-leaping method
urn:miriam:doi:10.1063/1.1992473
KISAO
The explicit tau-leaping procedure attempts to speed up the stochastic simulation of a chemically reacting system by approximating the number of firings of each reaction channel during a chosen time increment Tau as a Poisson random variable. Since the Poisson random variable can have arbitrarily large sample values, there is always the possibility that this procedure will cause one or more reaction channels to fire so many times during Tau that the population of some reactant species will be driven negative. Two recent papers have shown how that unacceptable occurrence can be avoided by replacing the Poisson random variables with binomial random variables, whose values are naturally bounded. This paper describes a modified Poisson tau-leaping procedure that also avoids negative populations, but is easier to implement than the binomial procedure. The new Poisson procedure also introduces a second control parameter, whose value essentially dials the procedure from the original Poisson tau-leaping at one extreme to the exact stochastic simulation algorithm at the other; therefore, the modified Poisson procedure will generally be more accurate than the original Poisson procedure [urn:miriam:biomodels.kisao:KISAO_0000040].
modified poisson tau-leaping
Fehlberg method
urn:miriam:doi:10.1007/BF02241732
urn:miriam:pubmed:14990450
E-Cell
JSim
KISAO
RKF45
Runge-Kutta-Fehlberg based method
The method was developed by the German mathematician Erwin Fehlberg and is based on the class of Runge-Kutta methods. The Runge-Kutta-Fehlberg method uses an O(h4) method together with an O(h5) method that uses all of the points of the O(h4) method, and hence is often referred to as an RKF45 method. Similar schemes with different orders have since been developed. By performing one extra calculation that would be required for an RK5 method, the error in the solution can be estimated and controlled and an appropriate step size can be determined automatically, making this method efficient for ordinary problems of automated numerical integration of ordinary differential equations.
VCell
iBioSim
Dormand-Prince method
2007-11-12
urn:miriam:doi:10.1016/0771-050X(80)90013-3
urn:miriam:pubmed:14990450
DP45
Dormand-Prince is an explicit method for the numerical integration of ODES with a given initial value.
ECell3
JSim
KISAO
Matlab
dk
iBioSim
LSODA
2007-11-30
http://www.nea.fr/abs/html/uscd1227.html
urn:miriam:doi:10.1137/0904010
urn:miriam:isbn:978-0444866073
KISAO
LSODA solves systems dy/dt = f with a dense or banded Jacobian when the problem is stiff, but it automatically selects between non-stiff (Adams [urn:miriam:biomodels.kisao:KISAO_0000289]) and stiff (BDF [urn:miriam:biomodels.kisao:KISAO_0000288]) methods. It uses the non-stiff method initially, and dynamically monitors data in order to decide which method to use.
Livermore solver for ordinary differential equations with automatic method switching
dk
LSODAR
2007-10-27
http://www.nea.fr/abs/html/uscd1228.html
urn:miriam:isbn:978-0444866073
KISAO
LSODAR is a variant of LSODA [urn:miriam:biomodels.kisao:KISAO_0000088] with a root finding capability added. Thus it solves problems dy/dt = f with dense or banded Jacobian and automatic method selection, and at the same time, it finds the roots of any of a set of given functions of the form g(t,y). This is often useful for finding stop conditions, or for finding points at which a switch is to be made in the function f.
Livermore solver for ordinary differential equations with automatic method switching and root finding
dk
ordinary differential equation solver for stiff or non-stiff systems with root finding
LSODI
urn:miriam:doi:10.1145/1218052.1218054
urn:miriam:isbn:978-0444866073
KISAO
LSODI solves systems given in linearly implicit form, including differential-algebraic systems.
Livermore solver for ordinary differential equations, implicit version
LSODIS
2007-11-30
http://www.nea.fr/abs/html/uscd1225.html
urn:miriam:isbn:978-0444866073
KISAO
LSODIS is a set of general-purpose FORTRAN routines solver for the initial value problem for ordinary differential equation systems. It is suitable for both stiff and nonstiff systems. LSODIS treat systems in the linearly implicit form A(t,y) dy/dt = g(t,y), A = a square matrix, i.e. with the derivative dy/dt implicit, but linearly so.
Livermore solver for ordinary differential equations, implicit sparse version
dk
LSODPK
2008-07-08
urn:miriam:isbn:978-0444866073
KISAO
LSODPK is a set of FORTRAN subroutines for solving the initial value problem for stiff and nonstiff systems of ordinary differential equations. In solving stiff systems, LSODPK uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods [urn:miriam:biomodels.kisao:KISAO_0000354]. The user must select the desired Krylov method and supply a pair of routine to evaluate, preprocess, and solve the (left and/or right) preconditioner matrices. Aside from preconditioning, the implementation is matrix-free, meaning that explicit storage of the Jacobian (or related) matrix is not required. The method is experimental because the scope of problems for which it is effective is not well-known, and users are forewarned that LSODPK may or may not be competitive with traditional methods on a given problem. LSODPK also includes an option for a user-supplied linear system solver to be used without Krylov iteration.
Livermore solver for ordinary differential equations for stiff and nonstiff systems with krylov corrector iteration
NLN
Livermore solver
2008-07-08
true
KISAO
Method to solve ordinary differential equations developed at the Lawrence Livermore National Laboratory.
NLN
sub-volume stochastic reaction-diffusion algorithm
2008-07-08
true
KISAO
NLN
Stochastic method using a combination of discretisation of compartment volumes into voxels and Gillespie-like algorithm [urn:miriam:biomodels.kisao:KISAO_0000241] to simulate the evolution of the system.
kinetic simulation algorithm characteristic
true
AZ
KISAO
Simulation algorithm property, which can, for example, describe the model, such as the type of variables (discrete or continuous), and information on the treatment of spatial descriptions, or can be a numerical characteristic, such as the system's behaviour (deterministic or stochastic) as well as the progression mechanism (fixed or adaptive time steps).
type of variable
true
KISAO
Type of variables used for the simulation.
type of system behaviour
true
A characteristic describing the rules the algorithm uses to simulate the temporal evolution of a system, specifically whether or not the final state is uniquely determined from a precise initial state.
KISAO
type of progression time step
true
KISAO
Type of time steps used by the algorithm.
spatial description
2008-07-08
Algorithm that takes into account the location of the reacting components.
KISAO
NLN
deterministic system behaviour
2008-07-08
Algorithm that simulates the temporal evolution of a system deterministically, so that from a precise initial state the algorithm will always end up in the same final state.
KISAO
NLN
stochastic system behaviour
2008-07-08
Algorithm that simulates the temporal evolution of a system using probabilistic rules, so that between two simulations, the same precise initial state may result in a different final state.
KISAO
NLN
discrete variable
2008-07-08
Algorithm that allows values of system's variables to change by discrete (integral) amounts.
KISAO
NLN
continuous variable
2008-07-08
Algorithm that allows the values of a system's variables to change by continuous (non-integral) amounts.
KISAO
NLN
progression with adaptive time step
2008-07-08
Algorithm that does not use fixed time steps to update the state of a system during the whole simulation, but on the contrary adapts the length of the time steps to the local situation.
KISAO
NLN
progression with fixed time step
2008-07-08
Algorithm that uses time steps of constant length to update the state of a system during the whole simulation.
KISAO
NLN
kinetic simulation algorithm parameter
true
AZ
KISAO
Parameter that can be used in the simulation experiment settings.
particle number lower limit
KISAO
This parameter of 'Pahle hybrid method' [urn:miriam:biomodels.kisao:KISAO_0000231] is a double value specifying the lower limit for particle numbers. Species with a particle number below this value are considered as having a low particle number. The 'particle number lower limit' cannot be higher than the 'particle number upper limit' [urn:miriam:biomodels.kisao:KISAO_0000204].
particle number upper limit
KISAO
This parameter of 'Pahle hybrid method' [urn:miriam:biomodels.kisao:KISAO_0000231] is a double value specifying the upper limit for particle numbers. Species with a particle number above this value are considered as having a high particle number. The 'particle number upper limit' cannot be lower than the 'particle number lower limit' [urn:miriam:biomodels.kisao:KISAO_0000203].
partitioning interval
KISAO
This positive integer value specifies after how many steps the internal partitioning of the system should be recalculated.
relative tolerance
KISAO
RTOL
This parameter is a numeric value specifying the desired relative tolerance the user wants to achieve. A smaller value means that the trajectory is calculated more accurately.
absolute tolerance
ATOL
KISAO
This parameter is a positive numeric value specifying the desired absolute tolerance the user wants to achieve.
integrate reduced model
KISAO
This parameter is a boolean value to determine whether the integration shall be performed using the mass conservation laws (true), i.e., reducing the number of system variables or to use the complete model (false).
LSODA maximum non-stiff order
Adams max order
KISAO
This parameter is a positive integer value specifying the maximal order the non-stiff Adams integration method [urn:miriam:biomodels.kisao:KISAO_0000289] shall attempt before switching to the stiff BDF method [urn:miriam:biomodels.kisao:KISAO_0000288].
LSODA maximum stiff order
BDF max order
KISAO
This parameter is a positive integer value specifying the maximal order the stiff BDF integration method [urn:miriam:biomodels.kisao:KISAO_0000288] shall attempt before switching to smaller internal step sizes.
number of history bins
KISAO
The 'number of history bins' is only enabled for models that contain delayed or multistep reactions for specifying the granularity with which the delayed reaction solver should retain the history of species values, for species that participate in delayed reactions.
tau-leaping epsilon
urn:miriam:doi:10.1063/1.1378322
KISAO
The leap condition is chosen such that the expected change in the propensity function aj(x) is bounded by Epsilon * a0 where Epsilon is an error control parameter between 0 and 1. This parameter is the basic error control mechanism for the Tau-Leaping algorithm [urn:miriam:biomodels.kisao:KISAO_0000039]. As Epsilon decreases the leaps become shorter and the simulation is more accurate.
epsilon
tolerance
minimum reactions per leap
'minimum reactions per leap' parameter is used in hybrid methods, which adaptively switch between the tau-leaping algorithm [urn:miriam:biomodels.kisao:KISAO_0000039] to the SSA Direct Method [urn:miriam:biomodels.kisao:KISAO_0000029] when the number of reactions in a single tau-leaping leap step is less than the threshold.
KISAO
threshold
Pahle hybrid method
urn:miriam:pubmed:17032683
AZ
COPASI
KISAO
The hybrid method combines the stochastic 'Gibson-Bruck's next reaction method' [urn:miriam:biomodels.kisao:KISAO_0000027] with different algorithms for the numerical integration of ODEs. The biochemical network is dynamically partitioned into a deterministic and a stochastic subnet depending on the current particle numbers in the system. The user can define limits for when a particle number should be considered low or high. The stochastic subnet contains reactions involving low numbered species as substrate or product. All the other reactions form the deterministic subnet. The two subnets are then simulated in parallel using the stochastic and deterministic solver, respectively. The reaction probabilities in the stochastic subnet are approximated as constant between two stochastic reaction events.
LSOIBT
urn:miriam:isbn:978-0444866073
KISAO
LSOIBT solves linearly implicit systems in which the matrices involved are all assumed to be block-tridiagonal. Linear systems are solved by the LU method.
Livermore solver for ordinary differential equations given in implicit form, with block-tridiagonal Jacobian treatment
LSODES
urn:miriam:isbn:978-0444866073
KISAO
LSODES solves systems dy/dt = f and in the stiff case treats the Jacobian matrix in general sparse form. It determines the sparsity structure on its own, or optionally accepts this information from the user. It then uses parts of the Yale Sparse Matrix Package (YSMP) to solve the linear systems that arise, by a sparse (direct) LU factorization/backsolve method.
Livermore solver for ordinary differential equations with general sparse Jacobian matrix
LSODKR
urn:miriam:isbn:978-0444866073
KISAO
LSODKR is an initial value ODE solver for stiff and nonstiff systems. It is a variant of the LSODPK [urn:miriam:biomodels.kisao:KISAO_0000093] and LSODE [urn:miriam:biomodels.kisao:KISAO_0000071] solvers, intended mainly for large stiff systems. The main differences between LSODKR and LSODE [urn:miriam:biomodels.kisao:KISAO_0000071] are the following: a) for stiff systems, LSODKR uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods. The user must supply routines for the preconditioning operations, b) within the corrector iteration, LSODKR does automatic switching between functional (fixpoint) iteration and modified Newton iteration, c) LSODKR includes the ability to find roots of given functions of the solution during the integration.
Livermore solver for ordinary differential equations, with preconditioned Krylov iteration methods for the Newton correction linear systems, and with root finding.
type of solution
true
Characteristic describing if the solution produced by the method is exact or approximate.
KISAO
exact solution
Algorithms providing exact solution.
KISAO
approximate solution
Approximation algorithms are algorithms used to find approximate solutions to optimization problems. Approximation algorithms are often associated with NP-hard problems; since it is unlikely that there can ever be efficient polynomial time exact algorithms solving NP-hard problems, one settles for polynomial time sub-optimal solutions. Unlike heuristics, which usually only find reasonably good solutions reasonably fast, one wants provable solution quality and provable run time bounds. Ideally, the approximation is optimal up to a small constant factor (for instance within 5% of the optimal solution). Approximation algorithms are increasingly being used for problems where exact polynomial-time algorithms are known but are too expensive due to the input size.
KISAO
type of method
true
Characteristic, describing if the method finds a solution by solving an equation involving only the current state of the system (explicit) or both the current and the later one (implicit).
KISAO
explicit method type
Explicit methods calculate the state of a system at a later time from the state of the system at the current time. Mathematically, if Y(t) is the current system state and Y((t+delta t) is the state at the later time (delta t is a small time step), then, for an explicit method Y(t+delta t) = F(Y(t)), to find Y(t+delta t).
KISAO
implicit method type
Implicit methods find a solution by solving an equation involving both the current state of the system and the later one. Mathematically, if Y(t) is the current system state and Y((t+delta t) is the state at the later time (delta t is a small time step), then, for an implicit method one solves an equation G(Y(t), Y(t+delta t))=0, to find Y(t+delta t).
KISAO
Gillespie-like method
true
Stochastic simulation algorithm using an approach alike the one described in Gillespie's papers of 1976 and 1977.
error control parameter
true
AZ
KISAO
Parameter controlling method accuracy.
method switching control parameter
true
AZ
KISAO
Parameters describing threshold conditions for algorithms that switch between different methods.
granularity control parameter
true
AZ
KISAO
Parameter controlling granularity.
tau-leaping delta
KISAO
Tau-leaping delta specifies how close two symmetric transition rates must be before we classify them as in partial-equilibrium. Only applies to the implicit tau routine [urn:miriam:biomodels.kisao:KISAO_0000045].
critical firing threshold
KISAO
The 'nonnegative Poisson tau-leaping method' [urn:miriam:biomodels.kisao:KISAO_0000084] is based on the fact that negative populations typically arise from multiple firings of reactions that are only a few firings away from consuming all the molecules of one of their reactants. To focus on those reaction channels, the modified tau-leaping algorithm introduces a second control parameter nc, a positive integer that is usually set somewhere between 5 and 20. Any reaction channel with a positive propensity function that is currently within nc firings of exhausting one of its reactants is then classified as a critical reaction. The modified algorithm chooses tau in such a way that no more than one firing of all the critical reactions can occur during the leap.
nonnegative tau-leaping second control parameter
partitioning control parameter
true
KISAO
Parameter describing partitioning of the system.
coarse-graining factor
urn:miriam:pubmed:15638577
KISAO
The time in each Monte-Carlo iteration of 'binomial tau-leaping method' [urn:miriam:biomodels.kisao:KISAO_0000074] is updated with the time increments tau=f/(a1+a2+...+aM). Here 1/(a1+a2+...+aM) is the averaged microscopic increment of the SSA [urn:miriam:biomodels.kisao:KISAO_0000029] and f is a coarse-graining factor, controlling the speed-up.
Brownian diffusion accuracy
Accuracy code of 'Brownian diffusion Smoluchowski method' [urn:miriam:biomodels.kisao:KISAO_0000057], which sets which neighbouring boxes are checked for potential bi-molecular reactions. Consider the reaction A + B -> C and suppose that A and B are within a binding radius of each other. This reaction will always be performed if A and B are in the same virtual box. If accuracy is set to at least 3, then it will also occur if A and B are in nearest-neighbour virtual boxes. If it is at least 7, then the reaction will happen if they are in nearest-neighbour boxes that are separated by periodic boundary conditions. And if it is 9 or 10, then all edge and corner boxes are checked for reactions, which means that no potential reactions are overlooked.
KISAO
Smoldyn
molecules per virtual box
KISAO
Smoldyn
Target molecules per virtual box is a parameter of 'Brownian diffusion Smoluchowski method' [urn:miriam:biomodels.kisao:KISAO_0000057], which sets the box sizes so that the average number of molecules per box, at simulation initiation, is close to the requested number.
virtual box side length
KISAO
Smoldyn
The 'virtual box side length' is a parameter of 'Brownian diffusion Smoluchowski method' [urn:miriam:biomodels.kisao:KISAO_0000057]. It requests the length of one side of a box.
surface-bound epsilon
A parameter of 'Brownian diffusion Smoluchowski method' [urn:miriam:biomodels.kisao:KISAO_0000057]. Molecules that are bound to a surface are given locations that are extremely close to that surface. However, this position does not need to be exactly at the surface, and in fact it usually cannot be exactly at the surface due to round-off error. The tolerance for how far a surface-bound molecule is allowed to be away from the surface can be set with the epsilon statement.
KISAO
neighbour distance
A parameter of 'Brownian diffusion Smoluchowski method' [urn:miriam:biomodels.kisao:KISAO_0000057]. When a surface-bound molecule diffuses off of one surface panel, it can sometimes diffuse onto the neighbouring surface tile. It does so only if the neighbouring panel is declared to be a neighbour and also the neighbour is within a distance that is set with the neighbour distance statement.
KISAO
virtual box size
KISAO
Target size of virtual boxes for 'Brownian diffusion Smoluchowski method' [urn:miriam:biomodels.kisao:KISAO_0000057].
Euler method
urn:miriam:isbn:052143064X
AZ
ByoDyn
JSim
KISAO
The Euler method, named after Leonhard Euler, is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value.
NFSim agent-based simulation method
2011-04-07
urn:miriam:doi:10.1038/nmeth.1546
A generalization a rule-based version of 'Gillespie's direct method' (SSA) [urn:miriam:biomodels.kisao:KISAO_0000029]. The method is guaranteed to produce the same results as the exact SSA [urn:miriam:biomodels.kisao:KISAO_0000029] by cycling over three primary steps. First, NFsim calculates the probability or propensity for each rule to take effect given the current molecular states. Second, it samples the time to the next reaction event and selects the corresponding reaction rule. Finally, NFsim executes the selected reaction by applying the rule and updating the molecular agents accordingly.
AZ
KISAO
NFSim
cellular automata update method
2011-04-07
urn:miriam:doi:10.1103/RevModPhys.55.601
AZ
CA
Cellular automata are mathematical idealizations of physical systems in which space and time are discrete, and physical quantities take on a finite set of discrete values. A cellular automaton consists of a regular uniform lattice (or ''array''), usually infinite in extent, with a discrete variable at each site (''cell''). A cellular automaton evolves in discrete time steps, with the value of the variable at one site being affected by the values of variables at sites in its ''neighbourhood'' on the previous time step. The neighbourhood of a site is typically taken to be the site itself and all immediately adjacent sites. The variables at each site are updated simultaneously (''synchronously''), based on the values of the variables in their neighbourhood at the preceding time step, and according to a definite set of ''local rules''.
KISAO
cellular automata
cellular spaces
cellular structures
homogeneous structures
iterative arrays
tessellation automata
tessellation structures
type of system state change
2011-05-05
true
AZ
KISAO
event-driven
2011-05-05
AZ
KISAO
The state of the system is evolved discontinuously in time from one event to another, predicting the time of the next event whenever an event is processed.
discrete event simulation
time-driven
2011-05-05
AZ
KISAO
The state of the system changes continuously in time and is evolved over a sequence of small time steps, discovering and processing events at the end of the time step.
synchronous event-driven
2011-05-05
AZ
In synchronous event-driven algorithms, there is a global simulation time t, typically the time when the last processed event occurred, and all of the particles are at the same time t.
KISAO
asynchronous event-driven
2011-05-05
AED
AZ
In asynchronous algorithms, there is a global simulation time t, typically the time when the last processed event occurred, and each particle is at a different point in time ti ≤ t, typically the last time it participated in an event.
KISAO
hard-particle molecular dynamics
2011-05-05
urn:miriam:doi:10.1016/j.jcp.2004.08.014
A collision-driven molecular dynamics algorithm for a system of non-spherical particles.
AZ
KISAO
first-passage Monte Carlo algorithm
2011-05-05
urn:miriam:doi:10.1103/PhysRevLett.97.230602
AED DKMC
AED diffusion kinetic Monte Carlo method
AZ
KISAO
We present a novel Monte Carlo algorithm for N diffusing finite particles that react on collisions. Using the theory of first-passage processes and time dependent Green's functions, we break the difficult N-body problem into independent single- and two-body propagations circumventing numerous diffusion hops used in standard Monte Carlo simulations. The new algorithm is exact, extremely efficient, and applicable to many important physical situations in arbitrary integer dimensions.
asynchronous event-driven diffusion Monte Carlo
Gill method
2011-05-09
urn:miriam:doi:10.1017/S0305004100026414
AZ
Gill's fourth order method is a Runge-Kutta method for approximating the solution of the initial value problem y'(x) = f(x,y); y(x0) = y0 which evaluates the integrand,f(x,y), four times per step. This method is a fourth order procedure for which Richardson extrapolation can be used.
Gill's method
KISAO
Runge-Kutta-Gill method
Metropolis Monte Carlo algorithm
2011-05-09
urn:miriam:doi:10.1063/1.1699114
A general method, suitable for fast computing machines, for investigating such properties as equations of state for substances consisting of interacting individual molecules is described. The method consists of a modified Monte Carlo integration [urn:miriam:biomodels.kisao:KISAO_0000051] over configuration space.
AZ
CompuCell3D
KISAO
Metropolis algorithm
Metropolis–Hastings algorithm
Adams–Bashforth method
2011-05-09
urn:miriam:isbn:978-3-540-56670-0
AZ
Given an initial value problem: y' = f(x,y), y(x0) = y0 together with additional starting values y1 = y(x0 + h), . . . , yk-1 = y(x0 + (k-1) h) the k-step Adams-Bashforth method is an explicit linear multistep method that approximates the solution, y(x) at x = x0+kh, of the initial value problem by yk = yk - 1 + h * ( a0 f(xk - 1,yk - 1) + a1 f(xk - 2,yk - 2) + . . . + ak - 1 f(x0,y0) ), where a0, a1, . . . , ak - 1 are constants.
KISAO
explicit Adams method
Adams-Moulton method
2011-05-09
urn:miriam:isbn:978-3-540-56670-0
AZ
KISAO
The (k-1)-step Adams-Moulton method is an implicit linear multistep method that iteratively approximates the solution, y(x) at x = x0+kh, of the initial value problem by yk = yk - 1 + h * ( b0 f(xk,yk) + b1 f(xk - 1,yk - 1) + . . . + bk - 1 f(x1,y1) ), where b1, . . . , bk - 1 are constants.
VCell
implicit Adams method
linear multistep method
2011-05-09
true
urn:miriam:isbn:978-3-540-56670-0
AZ
KISAO
Linear multistep methods are used for the numerical solution of ordinary differential equations. Conceptually, a numerical method starts from an initial point and then takes a short step forward in time to find the next solution point. The process continues with subsequent steps to map out the solution.
KINSOL
2011-05-09
urn:miriam:doi:10.1137/0911026
urn:miriam:doi:10.1145/1089014.1089020
AZ
FKINSOL
KINSOL is a solver for nonlinear algebraic systems based on Newton-Krylov solver technology [urn:miriam:biomodels.kisao:KISAO_0000354]. It is newly rewritten in the C language, based on the previous Fortran package NKSOL of Brown and Saad.
KISAO
NKSOL
Newton-Krylov solver for nonlinear algebraic systems
IDA
2011-05-09
urn:miriam:doi:10.1137/0915088
urn:miriam:doi:10.1145/1089014.1089020
AZ
IDA is a package for the solution of differential-algebraic equation (DAE) systems in the form F(t,y,y')=0. It is written in C, but derived from the package DASPK [urn:miriam:biomodels.kisao:KISAO_0000355] which is written in Fortran.
KISAO
VCell
solver for differential-algebraic equation systems
SUNDIALS method
2011-05-09
true
urn:miriam:doi:10.1145/1089014.1089020
AZ
KISAO
One of the methods, implemented in SUNDIALS (a suite of advanced computational codes for solving large-scale problems that can be modeled as a system of nonlinear algebraic equations, or as initial-value problems in ordinary differential or differential-algebraic equations).
finite volume method
2011-05-09
urn:miriam:isbn:0898715342
AZ
FVM
KISAO
The finite volume method is a method for representing and evaluating partial differential equations in the form of algebraic equations, which attempts to emulate continuous conservation laws of physics.
VCell
Euler–Maruyama method
2011-05-09
urn:miriam:doi:10.1098/rspa.2003.1247
AZ
KISAO
The Euler–Maruyama method is a method for the approximate numerical solution of a stochastic differential equation, which truncates the Ito and Stratonovich Taylor series of the exact solution after the first order stochastic terms. This converges to the Ito solution with strong global order accuracy 1/2 or weak global order accuracy 1. It is a simple generalization of the Euler method [urn:miriam:biomodels.kisao:KISAO_0000261] for ordinary differential equations to stochastic differential equations.
stochastic Euler scheme
Milstein method
2011-05-10
urn:miriam:isbn:079233213X
AZ
KISAO
The Milstein method is a technique for the approximate numerical solution of a stochastic differential equation.
backward differentiation formula
2011-05-10
urn:miriam:isbn:0136266061
AZ
BDF
ByoDyn
Gear method
Gear's method
KISAO
The backward differentiation formulas (BDF) are implicit multistep methods based on the numerical differentiation of a given function and are wildly used for integration of stiff differential equations.
iBioSim
Adams method
2011-05-10
urn:miriam:isbn:978-3-540-56670-0
AZ
Adams' methods are multi-step methods used for the numerical integration of initial value problems in Ordinary Differential Equations (ODE's). Adams' algorithm consists of two parts: firstly, a starting procedure which provides y1, ... , yk-1 ( approximations to the exact solution at the points x0 + h, ... , x0 + (k - 1)h ) and, secondly, a multistep formula to obtain an approximation to the exact solution y(x0 + kh). This is then applied recursively, based on the numerical approximation of k successive steps, to compute y(x0 + (k + 1)h).
ByoDyn
KISAO
Merson method
2011-05-10
http://nla.gov.au/nla.cat-vn870866
A five-stage Runge–Kutta method with fourth-order accuracy.
AZ
JSim
KISAO
KM
Kutta–Merson method
Merson's method
Runge-Kutta–Merson method
Hammer-Hollingsworth method
2011-05-10
urn:issn:0891-6837
AZ
KISAO
The numerical integration of ordinary differential equations by the use of Gaussian quadrature methods.
Lobatto method
2011-05-10
urn:issn:1088-6842(e)
AZ
KISAO
There are three families of Lobatto methods, called IIIA, IIIB and IIIC. These are named after Rehuel Lobatto. All are implicit Runge-Kutta methods, have order 2s − 2 and they all have c1 = 0 and cs = 1.
implicit Runge-Kutta method based on Lobatto quadrature
Butcher–Kuntzmann method
2011-05-10
urn:issn:1088-6842(e)
urn:miriam:doi:10.1002/zamm.19660460519
AZ
From a theoretical point of view, the Butcher–Kuntzmann Runge–Kutta methods belong to the best step-by-step methods for nonstiff problems. These methods integrate first-order initial-value problems by means of formulas based on Gauss–Legendre quadrature, and combine excellent stability features with the property of superconvergence at the step points.
Gauss method
KISAO
Heun method
2011-05-10
urn:miriam:isbn:978-3-540-56670-0
AZ
Heun's method
KISAO
The method is named after Karl L. W. M. Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It can be seen as extension of the Euler method [urn:miriam:biomodels.kisao:KISAO_0000261] into two-stage second-order Runge–Kutta method.
embedded Runge-Kutta method
2011-05-10
true
urn:miriam:isbn:978-3-540-56670-0
AZ
An embedded Runge-Kutta method is a method in which two Runge-Kutta estimates are obtained using the same auxiliary functions ki but with a different linear combination of these functions so that one estimate has an order one greater than the other.
KISAO
embedded RK
Zonneveld method
2011-05-10
http://trove.nla.gov.au/work/21424455
AZ
An embedded Runge-Kutta method, proposed by J.A. Zonneveld in 1964.
KISAO
Radau method
2011-05-11
urn:issn:1088-6842(e)
AZ
Implicit Runge-Kutta methods based on Radau quadrature.
JSim
KISAO
implicit Runge-Kutta method based on Radau quadrature
Verner method
2011-05-10
urn:miriam:doi:10.1137/0728027
AZ
KISAO
The first high order embedded Runge-Kutta formulas that avoid the drawback of giving identically zero error estimates for quadrature problems y' = f(x) were constructed by Verner in 1978.
Verner's method
Lagrangian sliding fluid element algorithm
2011-05-11
urn:miriam:pubmed:1449234
AZ
BTEX
Because the analytic solutions to the partial differential equations require convolution integration, solutions are obtained relatively efficiently by a fast numerical method. Our approach centers on the use of a sliding fluid element algorithm for capillary convection, with the time step set equal to the length step divided by the fluid velocity. Radial fluxes by permeation between plasma, interstitial fluid, and cells and axial diffusion exchanges within each time step are calculated analytically. The method enforces mass conservation unless there is regional consumption.
JSim
KISAO
LSFEA
blood-tissue exchange method
finite difference method
2011-05-11
urn:miriam:isbn:0898715342
AZ
FDM
KISAO
The finite difference method is based on local approximations of the partial derivatives in a Partial Differential Equation, which are derived by low order Taylor series expansions.
MacCormack method
2011-05-11
urn:miriam:doi:10.2514/2.6901
AZ
In computational fluid dynamics, the MacCormack method is a widely used discretization scheme for the numerical solution of hyperbolic partial differential equations. This second-order finite difference method [urn:miriam:biomodels.kisao:KISAO_0000307] is introduced by R. W. MacCormack in 1969.
JSim
KISAO
Crank–Nicolson method
2011-05-11
urn:miriam:doi:10.1007/BF02127704
AZ
In numerical analysis, the Crank–Nicolson method is a finite difference method [urn:miriam:biomodels.kisao:KISAO_0000307] used for numerically solving the heat equation and similar partial differential equations. It is a second-order method in time, implicit in time, and is numerically stable. The method was developed by John Crank and Phyllis Nicolson in the mid 20th century.
KISAO
method of lines
2011-05-11
urn:miriam:isbn:0126241309
AZ
KISAO
MOL
NMOL
NUMOL
The method of lines is a general technique for solving partial differential equations (PDEs) by typically using finite difference relationships for the spatial derivatives and ordinary differential equations for the time derivative.
type of domain geometry handling
true
KISAO
S-System power-law canonical differential equations solver
2011-05-20
urn:miriam:urn:doi:10.1137/0727042
AZ
E-Cell
ESSYNS GMA
KISAO
Ordinary differential equations can be recast into a nonlinear canonical form called an S-system. Evidence for the generality of this class comes from extensive empirical examples that have been recast and from the discovery that sets of differential equations and functions, recognized as among the most general, are special cases of S-systems. Identification of this nonlinear canonical form suggests a radically different approach to numerical solution of ordinary differential equations. By capitalizing on the regular structure of S-systems, efficient formulas for a variable-order, variable-step Taylor-series method are developed.
lattice gas automata
2011-05-23
urn:miriam:isbn:3-540-66973-6
AZ
KISAO
LGA
LGCA
Lattice gas automata methods are a series of cellular automata methods used to simulate fluid flows. From the LGCA, it is possible to derive the macroscopic Navier-Stokes equations.
lattice gas cellular automata
enhanced Greens function reaction dynamics
2011-05-23
urn:miriam:doi:10.1007/978-3-540-88562-7_3
AZ
GFRD [urn:miriam:biomodels.kisao:KISAO_0000058] decomposes the multibody reaction diffusion problem to a set of single and two body problems. Analytical solutions for two body reaction diffusion are available via Smoluchowski equation. eGFRD allows to solve each subproblem asynchronously by introducing the concept of first passage processes.
KISAO
eGFRD
enhanced Greens function reaction dynamics
E-Cell multi-algorithm simulation method
2011-05-23
urn:miriam:pubmed:14990450
A modular meta-algorithm with a discrete event scheduler that can incorporate any type of time-driven simulation algorithm. It was shown that this meta-algorithm can efficiently drive simulation models with different simulation algorithms with little intrusive modification to the algorithms themselves. Only a few additional methods to handle communications between computational modules are required.
AZ
E-Cell
KISAO
Gauss-Legendre Runge-Kutta method
2011-05-26
urn:miriam:isbn:960-8457-54-8
AZ
KISAO
Open Formula
So called 'Open Formula', two points formula, three points formula, four points formula, five points formula and six points formula of the Runge-Kutta method to solve the initial value problem of the ordinary differential equation. These formulas use the points and weights from the Gauss-Legendre Quadrature formulas for finding the value of the definite integral.
iBioSim
Monte Carlo method
2011-05-26
true
urn:miriam:doi:10.2307/2280232
AZ
KISAO
MC
Monte Carlo methods (or Monte Carlo experiments) are a class of computational algorithms that rely on repeated random sampling to compute their results.
BioRica hybrid method
2011-05-26
urn:miriam:pubmed:19425152
AZ
BioRica
KISAO
The simulation schema for a given BioRica node is given by a hybrid algorithm that deals with continuous time and allows for discrete events that roll back the time according to these discrete interruptions.
Cash–Karp method
2011-05-26
urn:miriam:doi:10.1145/79505.79507
AZ
An family of explicit Runge-Kutta formulas, which are very efficient for problems with smooth solution as well as problems having rapidly varying solutions. Each member of this family consists of a fifty-order formula that contains embedded formulas of all orders 1 through 4. By computing solutions at several different orders, it is possible to detect sharp fronts or discontinuities before all the function evaluations defining the full Runge-Kutta step have been computed.
Cain
KISAO
hybridity
2011-05-27
AZ
KISAO
The basic idea of hybrid simulation methods is to combine the advantages of complementary simulation approaches: the whole system is subdivided into appropriate parts and different simulation methods operate on these parts at the same time.
equation-free probabilistic steady-state approximation
urn:miriam:doi:10.1063/1.2131050
2011-06-02
AZ
KISAO
We present a probabilistic steady-state approximation that separates the time scales of an arbitrary reaction network, detects the convergence of a marginal distribution to a quasi-steady-state, directly samples the underlying distribution, and uses those samples to accurately predict the state of the system, including the effects of the slow dynamics, at future times. The numerical method produces an accurate solution of both the fast and slow reaction dynamics while, for stiff systems, reducing the computational time by orders of magnitude. The developed theory makes no approximations on the shape or form of the underlying steady-state distribution and only assumes that it is ergodic. <...> The developed theory may be applied to any type of kinetic Monte Carlo simulation to more efficiently simulate dynamically stiff systems, including existing exact, approximate, or hybrid stochastic simulation techniques.
nested stochastic simulation algorithm
2011-06-02
urn:miriam:pubmed:16321076
AZ
KISAO
This multiscale method is a small modification of the Gillespie's direct method [urn:miriam:biomodels.kisao:KISAO_0000029], in the form of a nested SSA, with inner loops for the fast reactions, and outer loop for the slow reactions. The number of groups can be more than two, and the grouping into fast and slow variables can be done dynamically in an adaptive version of the scheme.
nested SSA
minimum fast/discrete reaction occurrences number
urn:miriam:doi:10.1063/1.2131050
2011-06-02
AZ
KISAO
Parameter of 'equation-free probabilistic steady-state approximation' method [urn:miriam:biomodels.kisao:KISAO_0000323], which describes the minimum number of fast/discrete reaction occurrences before their effects cause convergence to a quasi-steady-state distribution.
number of samples
urn:miriam:doi:10.1063/1.2131050
2011-06-02
AZ
KISAO
Parameter of 'equation-free probabilistic steady-state approximation' method [urn:miriam:biomodels.kisao:KISAO_0000323], which determines the number of samples taken from the distribution.
maximum discrete number
urn:miriam:doi:10.1063/1.2131050
2011-06-02
AZ
KISAO
Parameter of 'equation-free probabilistic steady-state approximation' method [urn:miriam:biomodels.kisao:KISAO_0000323], which controls the maximum number of molecules of some reactant species in order for the reaction to be considered discrete.
minimum fast rate
urn:miriam:doi:10.1063/1.2131050
2011-06-02
AZ
KISAO
Parameter of 'equation-free probabilistic steady-state approximation' method [urn:miriam:biomodels.kisao:KISAO_0000323], which controls the minimum rate of the reaction in order for it to be considered fast.
constant-time kinetic Monte Carlo algorithm
2011-06-03
urn:miriam:pubmed:18513044
AZ
KISAO
SSA-CR
The computational cost of the original SSA [urn:miriam:biomodels.kisao:KISAO_0000029] scaled linearly with the number of reactions in the network. Gibson and Bruck developed a logarithmic scaling version of the SSA which uses a priority queue or binary tree for more efficient reaction selection [urn:miriam:biomodels.kisao:KISAO_0000027]. More generally, this problem is one of dynamic discrete random variate generation which finds many uses in kinetic Monte Carlo and discrete event simulation. We present here a constant-time algorithm, whose cost is independent of the number of reactions, enabled by a slightly more complex underlying data structure.
R-leaping algorithm
2011-06-03
urn:miriam:pubmed:16964997
A novel algorithm is proposed for the acceleration of the exact stochastic simulation algorithm by a predefined number of reaction firings (R-leaping) that may occur across several reaction channels. In the present approach, the numbers of reaction firings are correlated binomial distributions and the sampling procedure is independent of any permutation of the reaction channels. This enables the algorithm to efficiently handle large systems with disparate rates, providing substantial computational savings in certain cases.
AZ
KISAO
R-leap method
exact R-leaping algorithm
2011-06-03
urn:miriam:pubmed:2852436
AZ
ER-leap method
KISAO
We present a SSA which, similar to R-leap [urn:miriam:biomodels.kisao:KISAO_0000330], accelerates SSA [urn:miriam:biomodels.kisao:KISAO_0000029] by executing multiple reactions per algorithmic step, but which samples the reactant trajectories from the same probability distribution as the SSA. This 'exact R-leap' or 'ER-leap' algorithm is a modification of the R-leap algorithm which is both exact and capable of substantial speed-up over SSA.
exact R-leap method
exact accelerated stochastic simulation algorithm
ER-leap initial leap
2011-06-03
urn:miriam:pubmed:2852436
AZ
L
KISAO
L (initial step) is a parameter of 'exact R-leaping method' [urn:miriam:biomodels.kisao:KISAO_0000331]. ''We will assume that the reaction event to be bounded occurs within a run of L events in the SSA algorithm[urn:miriam:biomodels.kisao:KISAO_0000029], in order to execute L reactions at once in the manner of the R-leap algorithm[urn:miriam:biomodels.kisao:KISAO_0000230]''.
accelerated stochastic simulation algorithm
2011-06-03
true
AZ
An algorithm, which accelerates SSA [urn:miriam:biomodels.kisao:KISAO_0000029] either at the expense of its accuracy or exact.
KISAO
accelerated SSA
multiparticle lattice gas automata
2011-06-03
urn:miriam:doi:10.1142/S0129183194000052
AZ
An algorithm which allows for an arbitrary number of particles, while keeping the benefits of the cellular automata approach [urn:miriam:biomodels.kisao:KISAO_0000315].
KISAO
multiparticle lattice gas cellular automata
generalized stochastic simulation algorithm
2011-06-03
true
AZ
Gillespie direct method [urn:miriam:biomodels.kisao:KISAO_0000029] follows unit-by-unit changes in the total numbers of each reactant species, it is especially well suited to the study of systems in which reactant densities are low and the application of methods based on continuum approximations, such as the traditional ordinary differential equations of chemical kinetics, is questionable. The 'generalized stochastic simulation algorithm' branch presents methods, which extend Gillespie direct method [urn:miriam:biomodels.kisao:KISAO_0000029] to suit to systems with other characteristics.
KISAO
D-leaping method
2011-06-03
urn:miriam:doi:10.1016/j.jcp.2009.05.004
AZ
KISAO
We propose a novel, accelerated algorithm for the approximate stochastic simulation of biochemical systems with delays. The present work extends existing accelerated algorithms by distributing, in a time adaptive fashion, the delayed reactions so as to minimize the computational effort while preserving their accuracy.
finite element method
2011-06-07
urn:miriam:doi:10.1109/MAP.2007.376627
A numerical technique for finding approximate solutions of partial differential equations (PDE) as well as of integral equations. The solution approach is based either on eliminating the differential equation completely (steady state problems), or rendering the PDE into an approximating system of ordinary differential equations, which are then numerically integrated using standard techniques such as Euler method [urn:miriam:biomodels.kisao:KISAO_0000261], Runge-Kutta [urn:miriam:biomodels.kisao:KISAO_0000064], etc.
AZ
FEA
FEM
KISAO
finite element analysis
h-version of the finite element method
2011-06-07
urn:miriam:doi:10.1016/0168-874X(94)90003-5
AZ
Classical form of the 'finite element method' [urn:miriam:biomodels.kisao:KISAO_0000337], in which polynomials of fixed degree p are used and the mesh is refined to increase accuracy. Can be considered as a special case of the h-p version [urn:miriam:biomodels.kisao:KISAO_0000340].
KISAO
h-FEM
h-method
p-version of the finite element method
2011-06-07
urn:miriam:doi:10.1137/0718033
AZ
KISAO
The p version of 'finite element method' [urn:miriam:biomodels.kisao:KISAO_0000337] uses a fixed mesh but increases the polynomial degree p to increase accuracy. Can be considered as a special case of the h-p version [urn:miriam:biomodels.kisao:KISAO_0000340].
p-FEM
p-method
h-p version of the finite element method
2011-06-07
urn:miriam:doi:10.1007/BF00272624
AZ
In h-p version of 'finite difference method' [urn:miriam:biomodels.kisao:KISAO_0000337] the two approaches of mesh refinement and degree enchacement are combined.
KISAO
hp-FEM
hp-method
mixed finite element method
2011-06-07
urn:miriam:doi:10.1016/0045-7825(90)90168-L
A 'finite element method' [urn:miriam:biomodels.kisao:KISAO_0000337] in which both stress and displacement fields are approximated as primary variables.
AZ
KISAO
level set method
2011-06-07
urn:miriam:doi:10.1016/0021-9991(88)90002-2
AZ
An algorithm for moving surfaces under their curvature. This algorithm rely on numerically solving Hamilton-Jacobi equations with viscous terms, using approximation techniques from hyperbolic conservation laws.
KISAO
LSM
level-set method
generalized finite element method
2011-06-07
urn:miriam:doi:10.1142/S0219876204000083
AZ
GFEM
KISAO
PUM
The GFEM is a generalization of the classical 'finite element method' [urn:miriam:biomodels.kisao:KISAO_0000337] — in its h [urn:miriam:biomodels.kisao:KISAO_0000338], p [urn:miriam:biomodels.kisao:KISAO_0000339], and h-p versions [urn:miriam:biomodels.kisao:KISAO_0000340]— as well as of the various forms of meshless methods used in engineering.
partition of unity method
h-p cloud method
2011-06-09
urn:miriam:doi:10.1002/(SICI)1098-2426(199611)12:6<673::AID-NUM3>3.0.CO;2-P
A meshless method, which uses a partition of unity to construct the family of h-p cloud functions.
AZ
KISAO
h-p clouds
method of clouds
mesh-based
In most large-scale numerical simulations of physical phenomena, a large percentage of the overall computational effort is expended on technical details connected with meshing. These details include, in particular, grid generation, mesh adaptation to domain geometry, element or cell connectivity, grid motion and separation to model fracture, fragmentation, free surfaces, etc.
meshless
Most meshless methods require a scattered set of nodal points in the domain of interest. In these methods, there may be no fixed connectivities between the nodes, unlike the finite element or finite difference methods. This feature has significant implications in modeling some physical phenomena that are characterized by a continuous change in the geometry of the domain under analysis.
extended finite element method
2011-06-09
urn:miriam:doi:10.1007/s00466-002-0391-2
A numerical method to model arbitrary discontinuities in continuous bodies that does not require the mesh to conform to the discontinuities nor significant mesh refinement near singularities. In X-FEM the standard finite element approximation [urn:miriam:biomodels.kisao:KISAO_0000337] is enriched and the approximation space is extended by an additional family of functions.
AZ
KISAO
X-FEM
XFEM
method of finite spheres
2011-06-09
urn:miriam:doi:10.1007/s004660050481
AZ
KISAO
MFS
Method of finite spheres is truly meshless in the sense that the nodes are placed and the numerical integration is performed without a mesh. Some of the novel features of the method of finite spheres are the numerical integration scheme and the way in which the Dirichlet boundary conditions are incorporated.
probability-weighted dynamic Monte Carlo method
2011-06-09
urn:miriam:doi:10.1021/jp011404w
AZ
KISAO
PW-DMC
We have developed a probability-weighted DMC method by incorporating the weighted sampling algorithm of equilibrium molecular simulations. This new algorithm samples the slow reactions very efficiently and makes it possible to simulate in a computationally efficient manner the reaction kinetics of physical systems in which the rates of reactions vary by several orders of magnitude.
probability-weighted DMC
multinomial tau-leaping method
2011-06-09
urn:miriam:pubmed:17343434
AZ
KISAO
MtauL
The multinomial tau-leaping method is an extension of the binomial tau-leaping method [urn:miriam:biomodels.kisao:KISAO_0000074] to networks with arbitrary multiple-channel reactant dependencies. Improvements were achieved by a combination of three factors: First, tau-leaping steps are determined simply and efficiently using a-priori information and Poisson distribution based estimates of expectation values for reaction numbers. Second, networks are partitioned into closed groups of reactions and corresponding reactants in which no group reactant set is found in any other group. Third, product formation is factored into upper bound estimation of the number of times a particular reaction occurs.
hybrid method
2011-06-09
true
A simulation methods which combines the advantages of complementary simulation approaches: the whole system is subdivided into appropriate parts and different simulation methods operate on these parts at the same time.
AZ
KISAO
generalized minimal residual algorithm
2011-06-10
urn:miriam:doi:10.1137/0907058
AZ
An iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace. It can be considered as a generalization of MINRES algorithm and is theoretically equivalent to the Generalized Conjugate Residual method and to ORTHODIR. The new algorithm presents several advantages over GCR and ORTHODIR.
GMRES
KISAO
Krylov subspace projection method
2011-06-10
urn:miriam:isbn:0898715342
AZ
KISAO
Krylov subspace method
Krylov subspace method is an iterative linear equation method, which builds up Krylov subspaces and look for good approximations to eigenvectors and invariant subspaces within the Krylov spaces.
DASPK
2011-06-10
urn:miriam:doi:10.1137/0915088
AZ
DDASPK
In DASPK, we have combined the time-stepping methods of DASSL [urn:miriam:biomodels.kisao:KISAO_0000255] with preconditioned iterative method GMRES [urn:miriam:biomodels.kisao:KISAO_0000353], for solving large-scale systems of DAEs of the form F(t, y, y') = 0, where F, y, y' are N-dimensional vectors, and a consistent set of initial conditions y(t0) = y0, y'(t0) = y'0 is given.
KISAO
SDASPK
differential algebraic system solver with Krylov preconditioning
DASSL
2011-06-10
http://www.nea.fr/abs/html/nesc9918.html
AZ
DASSL is designed for the numerical solution of implicit systems of differential/algebraic equations written in the form F(t,y,y')=0, where F, y, and y' are vectors, and initial values for y and y' are given.
DDASSL
KISAO
SDASSL
differential algebraic system solver
conjugate gradient method
2011-06-10
urn:issn:0091-0635
AZ
CG
Conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is symmetric and positive-definite. The conjugate gradient method is an iterative method, so it can be applied to sparse systems that are too large to be handled by direct methods. Such systems often arise when numerically solving partial differential equations.
KISAO
biconjugate gradient method
2011-06-10
urn:miriam:doi:10.1007/BFb0080109
AZ
BiCG
KISAO
The biconjugate gradient method provides a generalization of conjugate gradient method [urn:miriam:biomodels.kisao:KISAO_0000357] to non-symmetric matrices.
implicit-state Doob-Gillespie algorithm
2011-06-13
urn:miriam:isbn:3-540-76636-7 978-3-540-76636-0
AZ
KISAO
The algorithm uses a representation of the system together with a super-approximation of its ‘event horizon’ (all events that may happen next), and a specific correction scheme to obtain exact timings. Being completely local and not based on any kind of enumeration, this algorithm has a per event time cost which is independent of (i) the size of the set of generable species (which can even be infinite), and (ii) independent of the size of the system (ie, the number of agent instances). The algorithm can be refined, using concepts derived from the classical notion of causality, so that in addition to the above one also has that the even cost is depending (iii) only logarithmically on the size of the model (ie, the number of rules).
rule-based simulation method
2011-06-13
true
AZ
KISAO
Rule-based models provide a powerful alternative to approaches that require explicit enumeration of all possible molecular species of a system. Such models consist of formal rules governing interactive behaviour. Rule-based simulation methods are methods, used to simulated such models.
Adams predictor-corrector method
2011-06-16
urn:asin:B0000EFQ8B
AZ
KISAO
The combination of evaluating a single explicit integration method ('Adams–Bashforth method' [urn:miriam:biomodels.kisao:KISAO_0000279]) (the predictor step) in order to provide a good initial guess for the successive evaluation of an implicit method ('Adams-Moulton method' [urn:miriam:biomodels.kisao:KISAO_0000280]) (the corrector step) using iteration.
NDSolve method
2011-06-16
urn:miriam:isbn:978-1-57955-058-5
AZ
KISAO
Mathematica
The Mathematica computation system function NDSolve is a general numerical differential equation solver. It can handle a wide range of ordinary differential equations as well as some partial differential equations. NDSolve can also solve some differential-algebraic equations, which are typically a mix of differential and algebraic equations.
symplecticness
2011-06-16
urn:miriam:doi:10.1017/S0962492900002282
AZ
KISAO
Roughly speaking, ‘symplecticness’ is a characteristic property possessed by the solutions of Hamiltonian problems. A numerical method is called symplectic if, when applied to Hamiltonian problems, it generates numerical solutions which inherit the property of symplecticness (phase volume preservation).
partitioned Runge-Kutta method
2011-06-16
AZ
If a Hamiltonian system possesses a natural partitioning, it is possible to integrate its certain components using one Runge-Kutta method and other components using a different Runge-Kutta method. The overall s-stage scheme is called a partitioned Runge-Kutta method.
KISAO
PRK
SPRK
symplectic partitioned Runge-Kutta method
urn:miriam:doi:10.1007/BF01389456
partial differential equation discretization method
2011-06-27
true
A method which solves partial differential equations by discretizing them, i.e. approximating them by equations that involve a finite number of unknowns.
AZ
KISAO