Stability in Training PINNs for Stiff PDEs: Why Initial Conditions Matter

[2404.16189] Stability in Training PINNs for Stiff PDEs: Why Initial Conditions Matter Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Numerical Analysis arXiv:2404.16189 (math) [Submitted on 24 Apr 2024 ( v1 ), last revised 15 Aug 2026 (this version, v4)] Title: Stability in Training PINNs for Stiff PDEs: Why Initial Conditions Matter Authors: Baoli Hao , Chun Liu , Ulisses Braga-Neto , Lifan Wang , Ming Zhong View a PDF of the paper titled Stability in Training PINNs for Stiff PDEs: Why Initial Conditions Matter, by Baoli Hao and 4 other authors View PDF HTML (experimental) Abstract: Training physics-informed neural networks (PINNs) on stiff, time-dependent PDEs remains a fundamental challenge due to optimization instabilities and gradient pathologies. Through a series of rigorous ablation studies and Neural Tangent Kernel (NTK) analysis, we identify that the exact enforcement of initial conditions (ICs) is a decisive factor in stabilizing the training landscape. We present the first systematic ablation of two core strategies: hard initial-condition constrained transformation and self-adaptive loss weighting. Our findings demonstrate that embedding ICs directly into the network architecture provides an implicit time-marching effect, effectively reducing spectral bias and enabling the solution of highly stiff benchmarks, including sharp transitions and high-frequency coupled systems, primarily under periodic boundary conditions, with a Dirichlet extension reported as an additional robustness check. This work provides a scalable framework for developing reliable and physically-consistent neural solvers for complex mechanical systems. Subjects: Numerical Analysis (math.NA) MSC classes: 65M12, 65M75 Cite as: arXiv:2404.16189 [math.NA] (or arXiv:2404.16189v4 [math.NA] for this version) https://doi.org/10.48550/arXiv.2404.16189 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.3934/fods.2026016 Focus to learn more DOI(s) linking to related resources Submission history From: Baoli Hao [ view email ] [v1] Wed, 24 Apr 2024 20:26:34 UTC (2,659 KB) [v2] Sat, 17 May 2025 04:16:17 UTC (2,414 KB) [v3] Wed, 8 Oct 2025 01:52:47 UTC (2,517 KB) [v4] Sat, 15 Aug 2026 17:51:13 UTC (3,479 KB) Full-text links: Access Paper: View a PDF of the paper titled Stability in Training PINNs for Stiff PDEs: Why Initial Conditions Matter, by Baoli Hao and 4 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2024-04 Change to browse by: cs cs.NA math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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