SymPlex: A Structure-Aware Transformer for Symbolic PDE Solving
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917245902389248 |
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| author | Park, Yesom Lu, Annie C. Huang, Shao-Ching Hu, Qiyang Ju, Y. Sungtaek Osher, Stanley |
| author_facet | Park, Yesom Lu, Annie C. Huang, Shao-Ching Hu, Qiyang Ju, Y. Sungtaek Osher, Stanley |
| contents | We propose SymPlex, a reinforcement learning framework for discovering analytical symbolic solutions to partial differential equations (PDEs) without access to ground-truth expressions. SymPlex formulates symbolic PDE solving as tree-structured decision-making and optimizes candidate solutions using only the PDE and its boundary conditions. At its core is SymFormer, a structure-aware Transformer that models hierarchical symbolic dependencies via tree-relative self-attention and enforces syntactic validity through grammar-constrained autoregressive decoding, overcoming the limited expressivity of sequence-based generators. Unlike numerical and neural approaches that approximate solutions in discretized or implicit function spaces, SymPlex operates directly in symbolic expression space, enabling interpretable and human-readable solutions that naturally represent non-smooth behavior and explicit parametric dependence. Empirical results demonstrate exact recovery of non-smooth and parametric PDE solutions using deep learning-based symbolic methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03816 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | SymPlex: A Structure-Aware Transformer for Symbolic PDE Solving Park, Yesom Lu, Annie C. Huang, Shao-Ching Hu, Qiyang Ju, Y. Sungtaek Osher, Stanley Machine Learning We propose SymPlex, a reinforcement learning framework for discovering analytical symbolic solutions to partial differential equations (PDEs) without access to ground-truth expressions. SymPlex formulates symbolic PDE solving as tree-structured decision-making and optimizes candidate solutions using only the PDE and its boundary conditions. At its core is SymFormer, a structure-aware Transformer that models hierarchical symbolic dependencies via tree-relative self-attention and enforces syntactic validity through grammar-constrained autoregressive decoding, overcoming the limited expressivity of sequence-based generators. Unlike numerical and neural approaches that approximate solutions in discretized or implicit function spaces, SymPlex operates directly in symbolic expression space, enabling interpretable and human-readable solutions that naturally represent non-smooth behavior and explicit parametric dependence. Empirical results demonstrate exact recovery of non-smooth and parametric PDE solutions using deep learning-based symbolic methods. |
| title | SymPlex: A Structure-Aware Transformer for Symbolic PDE Solving |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.03816 |