SciMLBase Interface

PIDEProblem and ParabolicPDEProblem are out-of-place SciMLBase.AbstractSciMLProblem implementations. Their state x and all sampled states must use a numeric container compatible with the SciML array interface: it must support broadcast, preserve an appropriate element type, and support the mutating array operations required by the selected solver. The time span uses floating-point endpoints because HighDimPDE's adaptive and stochastic solver paths perform floating-point time arithmetic.

The condition and coefficient functions must accept the signatures documented on each problem constructor. PIDEProblem.f receives both sampled states and their values and gradients; ParabolicPDEProblem.f receives a state, value, gradient, parameters, and time. Both problem types are out-of-place, so these functions return their result rather than writing to a first output argument.

Use generic SciMLBase operations to work with the problem after construction. In particular, import solve from SciMLBase, rather than relying on a reexport, and use remake to replace problem data without reconstructing the complete problem manually.

using HighDimPDE
using LinearAlgebra: I
using SciMLBase: isinplace, remake, solve

μ(x, p, t) = zero(x)
σ(x, p, t) = I
g(x) = sum(abs2, x)
f(x, u, du, p, t) = zero(u)

prob = ParabolicPDEProblem(μ, σ, zeros(2), (0.0, 1.0); g, f)
@assert !isinplace(prob)
prob_with_parameters = remake(prob; p = [1.0])