Geometric Integrators for SDE problems

Specific Domains Modelling & Simulations
1

Hi,
I am trying to figure out how to use an SDE solver for matrix-valued Stochastic Differential Equations. It looks like the packages GeometricIntegrators.jl, and StochasticIntegrators.jl might have the functionality but I don’t understand how to use them. I have been using DifferentialEquations.jl for univariate SDEs with good success but this fails:

using DifferentialEquations, GeometricIntegratorsDiffEq
prob = SDEProblem(drift, diff, u0, tspan, p=p)
sol = solve(prob,GIEuler())

throws this error:

ERROR: Incompatible problem+solver pairing.
For example, this can occur if an ODE solver is passed with an SDEProblem.
Solvers are only capable of handling specific problem types. Please double
check that the chosen pairing is capable for handling the given problems.

Problem type: SDEProblem
Solver type: GIEuler
Problem types compatible with the chosen solver: ODEProblem

So is there a way to use Geometric Integrators on SDEs in Julia? If so, could someone share a toy example with the correct syntax?

Thanks,
Simone.

2

The solvers from the package are only for ODEs.

But you could use some of these solvers: SDE Solvers · DifferentialEquations.jl
with the keyword symplectic=true.

3

None of those ones are for SDEs, you chose methods for SDEs. As @SteffenPL said, the only geometric integrators in the package are the symplectic form of the midpoint explicit methods. There are many more methods that could be implemented here, but sadly they are not.

4

OK, thanks! Not sure if the symplectic methods are apporpriate for my problem, but I will definitely explore them. Thanks again for your help and answers.

Simone.