CUDA & Python for numerical integration and solving differential equations

Question

Can anyone please suggest some libraries which allow use CUDA in Python for numerical integration and/or solving of differential equations?

My goal is to solve large (~1000 equations) of coupled non-linear ordinary differential equations and I would like to use CUDA for it.

Answer 1

Julia's DifferentialEquations.jl is all GPU-compatible. If you make your arrays GPU-based arrays, then the solver recompiles to be all on the GPU (no data transfers). For example:

using OrdinaryDiffEq, CUDA, LinearAlgebra
u0 = cu(rand(1000))
A  = cu(randn(1000,1000))
f(du,u,p,t)  = mul!(du,A,u)
prob = ODEProblem(f,u0,(0.0f0,1.0f0)) # Float32 is better on GPUs!
sol = solve(prob,Tsit5())

is all GPU-based. You can make use of this from Python via diffeqpy. There's not much nice syntax exposing GPU usage to Python right now, but you could use the following to do the same:

import diffeqpy
diffeqpy.install()
from diffeqpy import de

sol = Main.eval("""
    using CUDA, LinearAlgebra
    u0 = cu(rand(1000))
    A  = cu(randn(1000,1000))
    f(du,u,p,t)  = mul!(du,A,u)
    prob = ODEProblem(f,u0,(0.0f0,1.0f0)) # Float32 is better on GPUs!
    sol = solve(prob,Tsit5())
    Array(sol) # Return an array
""")

Note that this requires CUDA is installed on your Julia installation.

Answer 2

I have seen that people use

• CuPy; and
• scikit-cuda.

But, I don't see that any of those provide differential equations capabilities.

Looking around, I found CudaPyInt and it uses PyCuda.