Compatibility

Not every combination of laws, spaces, time, solvers, and backends is valid. This page is generated from the declarations that validation reads, so it always agrees with what the compilers accept.

Laws

Every law states what it requires of a system, and every solver and backend declares the laws it supports. Validation reports a law that the chosen solver or backend does not support.

Law	Solvers	Backends
BilinearLaw	KineticSolver, RK4Solver, ScipyODESolver	NumpyBackend, NumbaBackend
BoundaryLaw	MonteCarloSolver, MesaSolver, CoSimulationSolver, IterationSolver, CaputoSolver, FractionalABMSolver, GrunwaldLetnikovSolver, L1Solver, GillespieSolver, LatticeSolver, CrankNicolsonSolver, ETDRK4Solver, IMEX2Solver, IMEXEulerSolver, LammpsSolver, PontryaginSolver, RK4Solver, SSPRKSolver, ScipyODESolver, SplitSolver, VelocityVerletSolver, Yoshida4Solver, RenewalSolver, EulerMaruyamaSolver, FractionalEulerMaruyamaSolver, HeunSolver, MilsteinSolver	NumpyBackend, NumbaBackend
CascadeLaw	LatticeSolver	NumpyBackend, NumbaBackend
CrossingLaw	CoSimulationSolver, RK4Solver, ScipyODESolver, EulerMaruyamaSolver, FractionalEulerMaruyamaSolver, HeunSolver, MilsteinSolver	NumpyBackend, NumbaBackend
DissipatorLaw	JumpTrajectoriesSolver, LindbladSolver, OperatorSolver, UnitarySolver	NumpyBackend, NumbaBackend
DriveLaw	LatticeSolver	NumpyBackend, NumbaBackend
EmissionLaw	CoSimulationSolver, IterationSolver	NumpyBackend, NumbaBackend
EncounterLaw	KineticSolver, RK4Solver, ScipyODESolver, StrangSplittingSolver	NumpyBackend, NumbaBackend
EquationLaw	CoSimulationSolver, CaputoSolver, FractionalABMSolver, GrunwaldLetnikovSolver, L1Solver, CollocationSolver, LammpsSolver, PontryaginSolver, RK4Solver, ScipyODESolver, VelocityVerletSolver, Yoshida4Solver, RenewalSolver, RootSolver, EulerMaruyamaSolver, FractionalEulerMaruyamaSolver, HeunSolver, MilsteinSolver	NumpyBackend, NumbaBackend
ExtremalLaw	LatticeSolver	NumpyBackend, NumbaBackend
FluxLaw	CoSimulationSolver, CaputoSolver, FractionalABMSolver, GrunwaldLetnikovSolver, L1Solver, CollocationSolver, CrankNicolsonSolver, ETDRK4Solver, IMEX2Solver, IMEXEulerSolver, LammpsSolver, PontryaginSolver, RK4Solver, SSPRKSolver, ScipyODESolver, SemiLagrangianSolver, SplitSolver, StrangSplittingSolver, VelocityVerletSolver, RenewalSolver, EulerMaruyamaSolver, FractionalEulerMaruyamaSolver, HeunSolver, MilsteinSolver	NumpyBackend, NumbaBackend
FractionalNoiseLaw	CoSimulationSolver, LammpsSolver, RenewalSolver, EulerMaruyamaSolver, FractionalEulerMaruyamaSolver, HeunSolver, MilsteinSolver	NumpyBackend, NumbaBackend
GeneratorLaw	JumpTrajectoriesSolver, LindbladSolver, OperatorSolver, UnitarySolver	NumpyBackend, NumbaBackend
GradientStepLaw	GradientDescentSolver	none
JumpLaw	CoSimulationSolver, GillespieSolver, RK4Solver, RenewalSolver, EulerMaruyamaSolver	NumpyBackend, NumbaBackend
LocalRuleLaw	CoSimulationSolver, LatticeSolver	NumpyBackend, NumbaBackend
MatchLaw	MesaSolver, CoSimulationSolver	NumpyBackend, NumbaBackend
NoiseLaw	CoSimulationSolver, LammpsSolver, RenewalSolver, EulerMaruyamaSolver, FractionalEulerMaruyamaSolver, HeunSolver, MilsteinSolver	NumpyBackend, NumbaBackend
RateLaw	CoSimulationSolver, CaputoSolver, FractionalABMSolver, GrunwaldLetnikovSolver, L1Solver, CollocationSolver, CrankNicolsonSolver, ETDRK4Solver, IMEX2Solver, IMEXEulerSolver, LammpsSolver, PontryaginSolver, RK4Solver, SSPRKSolver, ScipyODESolver, SemiLagrangianSolver, SplitSolver, StrangSplittingSolver, VelocityVerletSolver, Yoshida4Solver, RenewalSolver, EulerMaruyamaSolver, FractionalEulerMaruyamaSolver, HeunSolver, MilsteinSolver	NumpyBackend, NumbaBackend
RuleLaw	MesaSolver, CoSimulationSolver	NumpyBackend, NumbaBackend
SampleLaw	MonteCarloSolver, CoSimulationSolver	NumpyBackend, NumbaBackend
TransferLaw	MesaSolver, CoSimulationSolver, IterationSolver, CaputoSolver, FractionalABMSolver, GrunwaldLetnikovSolver, L1Solver, GillespieSolver, CrankNicolsonSolver, ETDRK4Solver, IMEX2Solver, IMEXEulerSolver, RK4Solver, SSPRKSolver, ScipyODESolver, SplitSolver, EulerMaruyamaSolver, FractionalEulerMaruyamaSolver, HeunSolver, MilsteinSolver	NumpyBackend, NumbaBackend
TransitionLaw	CoSimulationSolver, IterationSolver	NumpyBackend, NumbaBackend
UpdateLaw	CoSimulationSolver, IterationSolver, LatticeSolver	NumpyBackend, NumbaBackend

Solvers

Every solver declares what it supports. Validation checks a chosen solver against the time, space, laws, noise structures, and derivative orders of a system, and names what it lacks. A diagonal noise draws one Wiener process per state, a shared noise drives several states with one process, a correlated noise draws the processes of a WienerProcessSpec with a covariance, and a conserved noise draws one process per link of the lattice of a field.

Solver	Form	Time	Space	Laws	Noise	Orders
MonteCarloSolver	Monte Carlo sampling	DiscreteTime	LatticeSpace, NetworkSpace	BoundaryLaw, SampleLaw	any	integer
MesaSolver	agent-based model	DiscreteTime	ContinuousSpace, LatticeSpace, NetworkSpace, no space	BoundaryLaw, MatchLaw, RuleLaw, TransferLaw	any	integer
CoSimulationSolver	co-simulation	ContinuousTime, DiscreteTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	BoundaryLaw, CrossingLaw, EmissionLaw, EquationLaw, FluxLaw, JumpLaw, LocalRuleLaw, MatchLaw, NoiseLaw, RateLaw, RuleLaw, SampleLaw, TransferLaw, TransitionLaw, UpdateLaw	conserved, correlated, diagonal, shared	fractional, integer
IterationSolver	discrete map	DiscreteTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	BoundaryLaw, EmissionLaw, TransferLaw, TransitionLaw, UpdateLaw	any	integer
CaputoSolver	fractional differential equations	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	BoundaryLaw, EquationLaw, FluxLaw, RateLaw, TransferLaw	any	fractional, integer
FractionalABMSolver	fractional differential equations	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	BoundaryLaw, EquationLaw, FluxLaw, RateLaw, TransferLaw	any	fractional, integer
GrunwaldLetnikovSolver	fractional differential equations	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	BoundaryLaw, EquationLaw, FluxLaw, RateLaw, TransferLaw	any	fractional, integer
L1Solver	fractional differential equations	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	BoundaryLaw, EquationLaw, FluxLaw, RateLaw, TransferLaw	any	fractional, integer
GillespieSolver	jump process	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	BoundaryLaw, JumpLaw, TransferLaw	any	integer
LatticeSolver	lattice dynamics	DiscreteTime	LatticeSpace, NetworkSpace	BoundaryLaw, CascadeLaw, DriveLaw, ExtremalLaw, LocalRuleLaw, UpdateLaw	any	integer
GradientDescentSolver	learning by gradient steps	DiscreteTime	no space	GradientStepLaw	any	integer
JumpTrajectoriesSolver	operator dynamics	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	DissipatorLaw, GeneratorLaw	any	integer
LindbladSolver	operator dynamics	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	DissipatorLaw, GeneratorLaw	any	integer
OperatorSolver	operator dynamics	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	DissipatorLaw, GeneratorLaw	any	integer
UnitarySolver	operator dynamics	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	DissipatorLaw, GeneratorLaw	any	integer
CollocationSolver	ordinary differential equations	ContinuousTime	no space	EquationLaw, FluxLaw, RateLaw	any	integer
CrankNicolsonSolver	ordinary differential equations	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	BoundaryLaw, FluxLaw, RateLaw, TransferLaw	any	integer
ETDRK4Solver	ordinary differential equations	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	BoundaryLaw, FluxLaw, RateLaw, TransferLaw	any	integer
IMEX2Solver	ordinary differential equations	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	BoundaryLaw, FluxLaw, RateLaw, TransferLaw	any	integer
IMEXEulerSolver	ordinary differential equations	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	BoundaryLaw, FluxLaw, RateLaw, TransferLaw	any	integer
KineticSolver	ordinary differential equations	ContinuousTime	LatticeSpace	BilinearLaw, EncounterLaw	any	integer
LammpsSolver	ordinary differential equations	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	BoundaryLaw, EquationLaw, FluxLaw, NoiseLaw, RateLaw	diagonal	integer
PontryaginSolver	ordinary differential equations	ContinuousTime	no space	BoundaryLaw, EquationLaw, FluxLaw, RateLaw	any	integer
RK4Solver	ordinary differential equations	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	BilinearLaw, BoundaryLaw, CrossingLaw, EncounterLaw, EquationLaw, FluxLaw, JumpLaw, RateLaw, TransferLaw	any	integer
SSPRKSolver	ordinary differential equations	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	BoundaryLaw, FluxLaw, RateLaw, TransferLaw	any	integer
ScipyODESolver	ordinary differential equations	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	BilinearLaw, BoundaryLaw, CrossingLaw, EncounterLaw, EquationLaw, FluxLaw, RateLaw, TransferLaw	any	integer
SemiLagrangianSolver	ordinary differential equations	ContinuousTime	LatticeSpace, PhaseSpace	FluxLaw, RateLaw	any	integer
SplitSolver	ordinary differential equations	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	BoundaryLaw, FluxLaw, RateLaw, TransferLaw	any	integer
StrangSplittingSolver	ordinary differential equations	ContinuousTime	LatticeSpace, PhaseSpace	EncounterLaw, FluxLaw, RateLaw	any	integer
VelocityVerletSolver	ordinary differential equations	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	BoundaryLaw, EquationLaw, FluxLaw, RateLaw	any	integer
Yoshida4Solver	ordinary differential equations	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	BoundaryLaw, EquationLaw, RateLaw	any	integer
RenewalSolver	renewal process	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	BoundaryLaw, EquationLaw, FluxLaw, JumpLaw, NoiseLaw, RateLaw	diagonal	integer
RootSolver	static solution	StaticTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	EquationLaw	any	integer
EulerMaruyamaSolver	stochastic differential equations	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	BoundaryLaw, CrossingLaw, EquationLaw, FluxLaw, JumpLaw, NoiseLaw, RateLaw, TransferLaw	conserved, correlated, diagonal, shared	integer
FractionalEulerMaruyamaSolver	stochastic differential equations	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	BoundaryLaw, CrossingLaw, EquationLaw, FluxLaw, FractionalNoiseLaw, NoiseLaw, RateLaw, TransferLaw	diagonal	integer
HeunSolver	stochastic differential equations	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	BoundaryLaw, CrossingLaw, EquationLaw, FluxLaw, NoiseLaw, RateLaw, TransferLaw	conserved, correlated, diagonal, shared	integer
MilsteinSolver	stochastic differential equations	ContinuousTime	CayleySpace, ContinuousSpace, LatticeSpace, MeshSpace, NetworkSpace, no space	BoundaryLaw, CrossingLaw, EquationLaw, FluxLaw, NoiseLaw, RateLaw, TransferLaw	diagonal	integer

Backends

Backends turn the compiled laws into numeric functions. Each declares the laws, noise structures, and derivative orders it lowers.

Backend	Laws	Noise	Orders
NumpyBackend	BilinearLaw, BoundaryLaw, CascadeLaw, CrossingLaw, DissipatorLaw, DriveLaw, EmissionLaw, EncounterLaw, EquationLaw, ExtremalLaw, FluxLaw, FractionalNoiseLaw, GeneratorLaw, JumpLaw, LocalRuleLaw, MatchLaw, NoiseLaw, RateLaw, RuleLaw, SampleLaw, TransferLaw, TransitionLaw, UpdateLaw	conserved, correlated, diagonal, shared	fractional, integer
NumbaBackend	BilinearLaw, BoundaryLaw, CascadeLaw, CrossingLaw, DissipatorLaw, DriveLaw, EmissionLaw, EncounterLaw, EquationLaw, ExtremalLaw, FluxLaw, FractionalNoiseLaw, GeneratorLaw, JumpLaw, LocalRuleLaw, MatchLaw, NoiseLaw, RateLaw, RuleLaw, SampleLaw, TransferLaw, TransitionLaw, UpdateLaw	conserved, correlated, diagonal, shared	fractional, integer