Abstract:Solving time-dependent Partial Differential Equations (PDEs) is one of the most critical problems in computational science. While Physics-Informed Neural Networks (PINNs) offer a promising framework for approximating PDE solutions, their accuracy and training speed are limited by two core barriers: gradient-descent-based iterative optimization over complex loss landscapes and non-causal treatment of time as an extra spatial dimension. We present Frozen-PINN, a novel PINN based on the principle of space-time separation that leverages random features instead of training with gradient descent, and incorporates temporal causality by construction. On eight PDE benchmarks, including challenges such as extreme advection speeds, shocks, and high dimensionality, Frozen-PINNs achieve superior training efficiency and accuracy over state-of-the-art PINNs, often by several orders of magnitude. Our work addresses longstanding training and accuracy bottlenecks of PINNs, delivering quickly trainable, highly accurate, and inherently causal PDE solvers, a combination that prior methods could not realize. Our approach challenges the reliance of PINNs on stochastic gradient-descent-based methods and specialized hardware, leading to a paradigm shift in PINN training and providing a challenging benchmark for the community.
| Comments: | Accepted as an oral presentation (top 1.13% of all submissions) at ICLR 2026 (60 pages) |
| Subjects: | Numerical Analysis (math.NA); Computational Engineering, Finance, and Science (cs.CE); Machine Learning (cs.LG) |
| Cite as: | arXiv:2405.20836 [math.NA] |
| (or arXiv:2405.20836v3 [math.NA] for this version) | |
| https://doi.org/10.48550/arXiv.2405.20836 arXiv-issued DOI via DataCite |
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| Journal reference: | The Fourteenth International Conference on Learning Representations, 2026 |
From: Chinmay Datar [view email]
[v1]
Fri, 31 May 2024 14:24:39 UTC (3,590 KB)
[v2]
Tue, 30 Sep 2025 15:20:28 UTC (5,360 KB)
[v3]
Wed, 15 Apr 2026 13:46:50 UTC (6,971 KB)
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