# Automated Translation and Accelerated Solving of Differential Equations on Multiple GPU Platforms

arXiv: https://arxiv.org/abs/2304.06835 · HTML: https://mlsanity.com/paper/2304.06835/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Apr 2023.

## Built on by (most cited first, 3 of 3)

- [Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraints](https://mlsanity.com/paper/2506.04171/) (2025)
- [End-to-End Probabilistic Framework for Learning with Hard Constraints](https://mlsanity.com/paper/2506.07003/) (2025)
- [GRADSOLVE: fast exact gradients for ODE ensembles on GPUs](https://mlsanity.com/paper/2609.02876/) (2026)

## Abstract (arXiv)

We demonstrate a high-performance vendor-agnostic method for massively parallel solving of ensembles of ordinary differential equations (ODEs) and stochastic differential equations (SDEs) on GPUs. The method is integrated with a widely used differential equation solver library in a high-level language (Julia's DifferentialEquations.jl) and enables GPU acceleration without requiring code changes by the user. Our approach achieves state-of-the-art performance compared to hand-optimized CUDA-C++ kernels while performing 20--100× faster than the vectorizing map (vmap) approach implemented in JAX and PyTorch. Performance evaluation on NVIDIA, AMD, Intel, and Apple GPUs demonstrates performance portability and vendor-agnosticism. We show composability with MPI to enable distributed multi-GPU workflows. The implemented solvers are fully featured -- supporting event handling, automatic differentiation, and incorporation of datasets via the GPU's texture memory -- allowing scientists to take advantage of GPU acceleration on all major current architectures without changing their model code and without loss of performance. We distribute the software as an open-source library https://github.com/SciML/DiffEqGPU.jl