cuPSS: a package for pseudo-spectral integration of stochastic PDEs

TL;DR

cuPSS is a CUDA C++ package that enables fast, GPU-accelerated pseudo-spectral integration of stochastic PDEs across multiple dimensions, addressing limitations of existing tools in speed, flexibility, and stochasticity integration.

Contribution

The paper introduces cuPSS, a GPU-accelerated pseudo-spectral solver for stochastic PDEs, offering improved speed and modularity over existing numerical integration packages.

Findings

cuPSS significantly outperforms traditional finite-difference and spectral solvers in speed.

It supports generic stochastic PDEs in 1D, 2D, and 3D on flat lattices.

Benchmark results demonstrate its efficiency and versatility.

Abstract

A large part of modern research, especially in the broad field of complex systems, relies on the numerical integration of PDEs, with and without stochastic noise. This is usually done with eiher in-house made codes or external packages like MATLAB, Mathematica, Fenicsx, OpenFOAM, Dedalus, and others. These packages rarely offer a good combination of speed, generality, and the option to easily add stochasticity to the system, while in-house codes depend on certain expertise to obtain good performance, and are usually written for each specific use case, sacrificing modularity and reusability. This paper introduces a package written in CUDA C++, thus enabling by default gpu acceleration, that performs pseudo-spectral integration of generic stochastic PDEs in flat lattices in one, two and three dimensions. This manuscript describes the basic functionality of cuPSS, with an example and benchmarking, showing that cuPSS offers a considerable improvement in speed over other popular finite-difference and spectral solvers.