{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/automated-translation-and-accelerated-solving","title":"Automated Translation and Accelerated Solving of Differential Equations on Multiple GPU Platforms","arxiv_id":"2304.06835","date":"2023-04-13","proceeding":null,"authors":["Utkarsh Utkarsh","Valentin Churavy","Yingbo Ma","Tim Besard","Prakitr Srisuma","Tim Gymnich","Adam R. Gerlach","Alan Edelman","George Barbastathis","Richard D. Braatz","Christopher Rackauckas"],"abstract":"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$\\times$ 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","url_abs":"https://arxiv.org/abs/2304.06835v3","url_pdf":"https://arxiv.org/pdf/2304.06835v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"automated-translation-and-accelerated-solving","repo_url":"https://github.com/sciml/diffeqgpu.jl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"automated-translation-and-accelerated-solving","repo_url":"https://github.com/utkarsh530/gpuodebenchmarks","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"jax","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2304.06835","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}