Optimization and generalization analysis for two-layer physics-informed neural networks without over-parametrization
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912496550412288 |
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| author | Zeng, Zhihan Gu, Yiqi |
| author_facet | Zeng, Zhihan Gu, Yiqi |
| contents | This work focuses on the behavior of stochastic gradient descent (SGD) in solving least-squares regression with physics-informed neural networks (PINNs). Past work on this topic has been based on the over-parameterization regime, whose convergence may require the network width to increase vastly with the number of training samples. So, the theory derived from over-parameterization may incur prohibitive computational costs and is far from practical experiments. We perform new optimization and generalization analysis for SGD in training two-layer PINNs, making certain assumptions about the target function to avoid over-parameterization. Given $ε>0$, we show that if the network width exceeds a threshold that depends only on $ε$ and the problem, then the training loss and expected loss will decrease below $O(ε)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16380 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimization and generalization analysis for two-layer physics-informed neural networks without over-parametrization Zeng, Zhihan Gu, Yiqi Machine Learning This work focuses on the behavior of stochastic gradient descent (SGD) in solving least-squares regression with physics-informed neural networks (PINNs). Past work on this topic has been based on the over-parameterization regime, whose convergence may require the network width to increase vastly with the number of training samples. So, the theory derived from over-parameterization may incur prohibitive computational costs and is far from practical experiments. We perform new optimization and generalization analysis for SGD in training two-layer PINNs, making certain assumptions about the target function to avoid over-parameterization. Given $ε>0$, we show that if the network width exceeds a threshold that depends only on $ε$ and the problem, then the training loss and expected loss will decrease below $O(ε)$. |
| title | Optimization and generalization analysis for two-layer physics-informed neural networks without over-parametrization |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2507.16380 |