Solvers

A solver steps a system through time, or solves it at once for a static system. get_supported_tags() of a solver class returns the times, spaces, and law kinds it supports. simulate compares them with the tags of the system before compiling, and rejects a solver that lacks one. Leave the solver out and the tags choose the default solver. The table lists the supported tags of every solver, grouped by the mathematical form it solves.

Solver	Form	Time	Space	Law kinds
MesaSolver	agent-based system	discrete	any	update
CoSimulationSolver	co-simulation	continuous, discrete	any	any
IterationSolver	discrete map	discrete	any	equation, jump, update
FractionalABMSolver	fractional differential equations	continuous	any	equation, rate, update
GrunwaldLetnikovSolver	fractional differential equations	continuous	any	equation, rate, update
L1Solver	fractional differential equations	continuous	any	equation, rate, update
GillespieSolver	jump process	continuous	any	jump, update
LatticeSolver	lattice dynamics	discrete	cell complex, hypergraph, lattice, network, phase space	update
GradientDescentSolver	learning by gradient steps	discrete	none	update
MonteCarloSolver	Monte Carlo sampling	discrete	cell complex, hypergraph, lattice, network, phase space	sampling
JumpTrajectoriesSolver	operator dynamics	continuous	any	rate
LindbladSolver	operator dynamics	continuous	any	rate
OperatorSolver	operator dynamics	continuous	any	rate
UnitarySolver	operator dynamics	continuous	any	rate
CollocationSolver	ordinary differential equations	continuous	none	equation, rate
CrankNicolsonSolver	ordinary differential equations	continuous	any	equation, rate, update
ETDRK4Solver	ordinary differential equations	continuous	any	equation, rate, update
EulerSolver	ordinary differential equations	continuous	none	rate, update
IMEX2Solver	ordinary differential equations	continuous	any	equation, rate, update
IMEXEulerSolver	ordinary differential equations	continuous	any	equation, rate, update
KineticSolver	ordinary differential equations	continuous	lattice, phase space	rate
LammpsSolver	ordinary differential equations	continuous	any	equation, noise, rate, update
PontryaginSolver	ordinary differential equations	continuous	none	equation, rate, update
RK4Solver	ordinary differential equations	continuous	any	equation, jump, rate, update
SSPRKSolver	ordinary differential equations	continuous	any	rate, update
ScipyODESolver	ordinary differential equations	continuous	any	equation, rate, update
SemiLagrangianSolver	ordinary differential equations	continuous	lattice, phase space	rate
SplitSolver	ordinary differential equations	continuous	any	equation, rate, update
StrangSplittingSolver	ordinary differential equations	continuous	lattice, phase space	rate
VelocityVerletSolver	ordinary differential equations	continuous	any	equation, rate, update
Yoshida4Solver	ordinary differential equations	continuous	any	equation, rate, update
RenewalSolver	renewal process	continuous	any	equation, jump, noise, rate, update
RewritingSolver	rewriting system	discrete	any	update
RootSolver	static solution	static	any	equation
EulerMaruyamaSolver	stochastic differential equations	continuous	any	equation, jump, noise, rate, update
FractionalEulerMaruyamaSolver	stochastic differential equations	continuous	any	equation, noise, rate, update
HeunSolver	stochastic differential equations	continuous	any	equation, noise, rate, update
MilsteinSolver	stochastic differential equations	continuous	any	equation, noise, rate, update

A compatible solver

A rate with a noise term returns a rate and a noise law, and EulerMaruyamaSolver supports both.

from skcomplex.core.components.elements import CompartmentElement
from skcomplex.core.components.interactions import RateInteraction
from skcomplex.core.components.system import System
from skcomplex.core.engine.runtime import simulate
from skcomplex.core.engine.solvers import EulerMaruyamaSolver

tank = CompartmentElement('tank', n=10.0)
decay = RateInteraction('decay', target='tank', state='n', rate=lambda s: -0.5 * s.target.n, noise=0.1)
system = System(elements=[tank], interactions=[decay])
sorted(system.get_tags().laws), sorted(EulerMaruyamaSolver.get_supported_tags().laws)
trajectory = simulate(system, until=1, solver=EulerMaruyamaSolver(), random_state=0)
round(trajectory.values('tank.n')[-1], 2)

(['noise', 'rate'], ['equation', 'jump', 'noise', 'rate', 'update'])
6.15

An incompatible solver

RK4Solver integrates deterministic equations and does not support the noise law kind.

from skcomplex.core.components.elements import CompartmentElement
from skcomplex.core.components.interactions import RateInteraction
from skcomplex.core.components.system import System
from skcomplex.core.engine.runtime import simulate
from skcomplex.core.engine.solvers import RK4Solver
from skcomplex.core.errors import TagError

tank = CompartmentElement('tank', n=10.0)
decay = RateInteraction('decay', target='tank', state='n', rate=lambda s: -0.5 * s.target.n, noise=0.1)
try:
    simulate(System(elements=[tank], interactions=[decay]), until=1, solver=RK4Solver())
except TagError as error:
    message = str(error)
message
assert 'laws noise' in message

The solver RK4Solver does not support the laws noise of the system. Pass a solver that supports them, or none for the default.