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arXiv · 2602.03816

SymPlex: A Structure-Aware Transformer for Symbolic PDE Solving

Yesom Park·Annie C. Lu·Shao-Ching Huang·Qiyang Hu·Y. Sungtaek Ju·Stanley Osher
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Abstract

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.

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Yesom Park, Annie C. Lu, Shao-Ching Huang, Qiyang Hu, Y. Sungtaek Ju, Stanley Osher. 2026-02-03. SymPlex: A Structure-Aware Transformer for Symbolic PDE Solving. https://arxiv.org/abs/2602.03816

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