GPU Parallel Solving of Stochastic Differential Equations

One major application of DiffEqGPU is for computing ensemble statistics of SDE solutions using EnsembleGPUArray. The following demonstrates using this technique to generate large ensembles of solutions for a diagonal noise SDE with a high order adaptive method:

using DiffEqGPU, CUDA, StochasticDiffEq

function lorenz(du, u, p, t)
    du[1] = p[1] * (u[2] - u[1])
    du[2] = u[1] * (p[2] - u[3]) - u[2]
    du[3] = u[1] * u[2] - p[3] * u[3]
end

function multiplicative_noise(du, u, p, t)
    du[1] = 0.1 * u[1]
    du[2] = 0.1 * u[2]
    du[3] = 0.1 * u[3]
end

CUDA.allowscalar(false)
u0 = Float32[1.0; 0.0; 0.0]
tspan = (0.0f0, 10.0f0)
p = (10.0f0, 28.0f0, 8 / 3.0f0)
prob = SDEProblem(lorenz, multiplicative_noise, u0, tspan, p)
const pre_p = [rand(Float32, 3) for i in 1:10_000]
prob_func = (prob, i, repeat) -> remake(prob, p = pre_p[i] .* p)
monteprob = EnsembleProblem(prob, prob_func = prob_func)
sol = solve(monteprob, SOSRI(), EnsembleGPUArray(CUDA.CUDABackend()), trajectories = 10_000,
    saveat = 1.0f0)

EnsembleSolution Solution of length 10000 with uType:
SciMLBase.RODESolution{Float32, 2, uType, Nothing, Nothing, Vector{Float32}, randType, SciMLBase.SDEProblem{Vector{Float32}, Tuple{Float32, Float32}, true, Vector{Float32}, Nothing, SciMLBase.SDEFunction{true, SciMLBase.FullSpecialize, typeof(Main.lorenz), typeof(Main.multiplicative_noise), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, typeof(Main.multiplicative_noise), Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, Nothing}, StochasticDiffEq.SOSRI, IType, SciMLBase.DEStats, Nothing} where {uType, randType, IType}