{"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/sk-pinn-accelerated-physics-informed-deep","title":"SK-PINN: Accelerated physics-informed deep learning by smoothing kernel gradients","arxiv_id":"2411.02411","date":"2024-10-20","proceeding":null,"authors":["Cunliang Pan","Chengxuan Li","Yu Liu","Yonggang Zheng","Hongfei Ye"],"abstract":"The automatic differentiation (AD) in the vanilla physics-informed neural networks (PINNs) is the computational bottleneck for the high-efficiency analysis. The concept of derivative discretization in smoothed particle hydrodynamics (SPH) can provide an accelerated training method for PINNs. In this paper, smoothing kernel physics-informed neural networks (SK-PINNs) are established, which solve differential equations using smoothing kernel discretization. It is a robust framework capable of solving problems in the computational mechanics of complex domains. When the number of collocation points gradually increases, the training speed of SK-PINNs significantly surpasses that of vanilla PINNs. In cases involving large collocation point sets or higher-order problems, SK-PINN training can be up to tens of times faster than vanilla PINN. Additionally, analysis using neural tangent kernel (NTK) theory shows that the convergence rates of SK-PINNs are consistent with those of vanilla PINNs. The superior performance of SK-PINNs is demonstrated through various examples, including regular and complex domains, as well as forward and inverse problems in fluid dynamics and solid mechanics.","url_abs":"https://arxiv.org/abs/2411.02411v2","url_pdf":"https://arxiv.org/pdf/2411.02411v2.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":"sk-pinn-accelerated-physics-informed-deep","repo_url":"https://github.com/pcl-china/sk-pinn","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2411.02411","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}