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DifferentialEquations.jl
Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differential-algebraic equations (DAEs), and more in Julia.
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There is CUDA.jl for working with NVidia graphics cards, but I don't know of AMD equivalents.
Sounds like an interesting project, please post how you go! I found this with library, may be useful https://github.com/vinhphunguyen/MPM-Julia