AMStraMGRAM: Adaptive Multi-cutoff Strategy Modification for ANaGRAM
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912656889217024 |
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| author | Schwencke, Nilo Rousselot, Cyriaque Shilova, Alena Furtlehner, Cyril |
| author_facet | Schwencke, Nilo Rousselot, Cyriaque Shilova, Alena Furtlehner, Cyril |
| contents | Recent works have shown that natural gradient methods can significantly outperform standard optimizers when training physics-informed neural networks (PINNs). In this paper, we analyze the training dynamics of PINNs optimized with ANaGRAM, a natural-gradient-inspired approach employing singular value decomposition with cutoff regularization. Building on this analysis, we propose a multi-cutoff adaptation strategy that further enhances ANaGRAM's performance. Experiments on benchmark PDEs validate the effectiveness of our method, which allows to reach machine precision on some experiments. To provide theoretical grounding, we develop a framework based on spectral theory that explains the necessity of regularization and extend previous shown connections with Green's functions theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_15998 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | AMStraMGRAM: Adaptive Multi-cutoff Strategy Modification for ANaGRAM Schwencke, Nilo Rousselot, Cyriaque Shilova, Alena Furtlehner, Cyril Machine Learning Artificial Intelligence Recent works have shown that natural gradient methods can significantly outperform standard optimizers when training physics-informed neural networks (PINNs). In this paper, we analyze the training dynamics of PINNs optimized with ANaGRAM, a natural-gradient-inspired approach employing singular value decomposition with cutoff regularization. Building on this analysis, we propose a multi-cutoff adaptation strategy that further enhances ANaGRAM's performance. Experiments on benchmark PDEs validate the effectiveness of our method, which allows to reach machine precision on some experiments. To provide theoretical grounding, we develop a framework based on spectral theory that explains the necessity of regularization and extend previous shown connections with Green's functions theory. |
| title | AMStraMGRAM: Adaptive Multi-cutoff Strategy Modification for ANaGRAM |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2510.15998 |