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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.18989 |
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| _version_ | 1866917031895367680 |
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| author | Sun, Yifei |
| author_facet | Sun, Yifei |
| contents | Nonlinear PDE solvers require fine space-time discretizations and local linearizations, leading to high memory cost and slow runtimes. Neural operators such as FNOs and DeepONets offer fast single-shot inference by learning function-to-function mappings and truncating high-frequency components, but they suffer from poor out-of-distribution (OOD) generalization, often failing on inputs outside the training distribution. We propose an adversarial teacher-student distillation framework in which a differentiable numerical solver supervises a compact neural operator while a PGD-style active sampling loop searches for worst-case inputs under smoothness and energy constraints to expand the training set. Using differentiable spectral solvers enables gradient-based adversarial search and stabilizes sample mining. Experiments on Burgers and Navier-Stokes systems demonstrate that adversarial distillation substantially improves OOD robustness while preserving the low parameter cost and fast inference of neural operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18989 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards Universal Solvers: Using PGD Attack in Active Learning to Increase Generalizability of Neural Operators as Knowledge Distillation from Numerical PDE Solvers Sun, Yifei Machine Learning Nonlinear PDE solvers require fine space-time discretizations and local linearizations, leading to high memory cost and slow runtimes. Neural operators such as FNOs and DeepONets offer fast single-shot inference by learning function-to-function mappings and truncating high-frequency components, but they suffer from poor out-of-distribution (OOD) generalization, often failing on inputs outside the training distribution. We propose an adversarial teacher-student distillation framework in which a differentiable numerical solver supervises a compact neural operator while a PGD-style active sampling loop searches for worst-case inputs under smoothness and energy constraints to expand the training set. Using differentiable spectral solvers enables gradient-based adversarial search and stabilizes sample mining. Experiments on Burgers and Navier-Stokes systems demonstrate that adversarial distillation substantially improves OOD robustness while preserving the low parameter cost and fast inference of neural operators. |
| title | Towards Universal Solvers: Using PGD Attack in Active Learning to Increase Generalizability of Neural Operators as Knowledge Distillation from Numerical PDE Solvers |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2510.18989 |