SymPlex: A Structure-Aware Transformer for Symbolic PDE Solving
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SymPlex introduces a novel reinforcement learning framework for deriving analytical solutions to partial differential equations (PDEs) without needing ground-truth data. It employs a structure-aware Transformer, SymFormer, to optimize solutions based solely on the PDE and its boundary conditions. This approach enables interpretable solutions that effectively handle non-smooth behaviors, offering a significant advancement over traditional numerical methods. Empirical tests show SymPlex accurately recovers complex PDE solutions, highlighting its potential for practical applications in mathematical modeling and engineering.
SymPlex: A New Approach to Symbolic PDE Solving
Researchers have introduced SymPlex, an innovative reinforcement learning framework designed to discover analytical symbolic solutions for partial differential equations (PDEs) without requiring ground-truth expressions. This approach formulates symbolic PDE solving as a tree-structured decision-making problem, optimizing candidate solutions based on the given PDE and its boundary conditions.
Core Technology: SymFormer
At the heart of SymPlex is SymFormer, a structure-aware Transformer that models hierarchical symbolic dependencies. This is accomplished through tree-relative self-attention mechanisms that help the model discern relationships between different components of symbolic expressions. Additionally, SymFormer employs grammar-constrained autoregressive decoding to ensure generated solutions maintain syntactic validity.
Empirical Results
Empirical evaluations of SymPlex indicate its capability to exactly recover non-smooth and parametric solutions to PDEs, setting it apart from conventional numerical and neural approaches that typically approximate solutions within discretized function spaces.
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📰 Original Source: https://arxiv.org/abs/2602.03816v1
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