Breakeven complexity: A new perspective on neural partial differential equation solvers
A new paper introduces the concept of breakeven complexity in evaluating neural solvers for partial differential equations (PDEs). This framework considers both the up-front costs of neural solvers and the performance of traditional methods. The findings suggest that neural solvers may be more effective for complex problems requiring significant computational resources.
- ▪Neural surrogate solvers for PDEs can offer significant speed advantages over traditional numerical methods.
- ▪The proposed breakeven complexity metric accounts for the costs associated with data generation and training of neural solvers.
- ▪Results indicate that neural PDE solvers become increasingly effective as the complexity of the problems increases.
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| Original publisher | arXiv cs.AI |
| Canonical URL | https://arxiv.org/abs/2605.15399 |
| Publication time | Mon, 18 May 2026 00:00:00 -0400 |
| Retrieval time | 2026-05-18T04:04:54.418Z |
| Last seen | 2026-05-18T04:04:54.418Z |
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Computer Science > Machine Learning arXiv:2605.15399 (cs) [Submitted on 14 May 2026] Title:Breakeven complexity: A new perspective on neural partial differential equation solvers Authors:Yijing Zhang, Nicholas Roberts, Tanya Marwah, Mikhail Khodak View a PDF of the paper titled Breakeven complexity: A new perspective on neural partial differential equation solvers, by Yijing Zhang and 3 other authors View PDF HTML (experimental) Abstract:Neural surrogate solvers of partial differential equations (PDEs) promise dramatic speedups over numerical methods, especially in scenarios requiring many solves.
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