{"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/pinnacle-a-comprehensive-benchmark-of-physics","title":"PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs","arxiv_id":"2306.08827","date":"2023-06-15","proceeding":null,"authors":["Zhongkai Hao","Jiachen Yao","Chang Su","Hang Su","Ziao Wang","Fanzhi Lu","Zeyu Xia","Yichi Zhang","Songming Liu","Lu Lu","Jun Zhu"],"abstract":"While significant progress has been made on Physics-Informed Neural Networks (PINNs), a comprehensive comparison of these methods across a wide range of Partial Differential Equations (PDEs) is still lacking. This study introduces PINNacle, a benchmarking tool designed to fill this gap. PINNacle provides a diverse dataset, comprising over 20 distinct PDEs from various domains, including heat conduction, fluid dynamics, biology, and electromagnetics. These PDEs encapsulate key challenges inherent to real-world problems, such as complex geometry, multi-scale phenomena, nonlinearity, and high dimensionality. PINNacle also offers a user-friendly toolbox, incorporating about 10 state-of-the-art PINN methods for systematic evaluation and comparison. We have conducted extensive experiments with these methods, offering insights into their strengths and weaknesses. In addition to providing a standardized means of assessing performance, PINNacle also offers an in-depth analysis to guide future research, particularly in areas such as domain decomposition methods and loss reweighting for handling multi-scale problems and complex geometry. To the best of our knowledge, it is the largest benchmark with a diverse and comprehensive evaluation that will undoubtedly foster further research in PINNs.","url_abs":"https://arxiv.org/abs/2306.08827v2","url_pdf":"https://arxiv.org/pdf/2306.08827v2.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":"abstracts"},"code_links":[{"paper_slug":"pinnacle-a-comprehensive-benchmark-of-physics","repo_url":"https://github.com/i207m/pinnacle","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"jax","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"pinnacle-a-comprehensive-benchmark-of-physics","repo_url":"https://gitlab.com/mia_jinns/pinn-multi-library-benchmark","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"benchmarking","task_name":"Benchmarking"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2306.08827","atlas_url":"https://app.syntology.ai/?focus=2306.08827","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2306.08827"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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