# SymPlex: A Structure-Aware Transformer for Symbolic PDE Solving

arXiv: https://arxiv.org/abs/2602.03816 · HTML: https://mlsanity.com/paper/2602.03816/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Interpretable and logic-guided RL, one of 15 directions in Deep reinforcement learning methods.
- Builds on 15 of its 37 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Placed in

- Deep reinforcement learning methods / [Interpretable and logic-guided RL](https://mlsanity.com/deeprl/interpretable-and-logic-guided-rl/)

## Builds on (most cited first, 15 of 15)

- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [A Survey of Machine Learning for Big Code and Naturalness](https://mlsanity.com/paper/1709.06182/) (2017)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [Tree Transformer: Integrating Tree Structures into Self-Attention](https://mlsanity.com/paper/1909.06639/) (2019)
- [Deep Learning and Symbolic Regression for Discovering Parametric Equations](https://mlsanity.com/paper/2207.00529/) (2022)
- [Finite Expression Method for Solving High-Dimensional Partial Differential Equations](https://mlsanity.com/paper/2206.10121/) (2022)
- [R2D2: Recursive Transformer based on Differentiable Tree for Interpretable Hierarchical Language Modeling](https://mlsanity.com/paper/2107.00967/) (2021)
- [A Neural-Guided Dynamic Symbolic Network for Exploring Mathematical Expressions from Data](https://mlsanity.com/paper/2309.13705/) (2023)
- [Symbolic Regression via Control Variable Genetic Programming](https://mlsanity.com/paper/2306.08057/) (2023)
- [Neural Implicit Solution Formula for Efficiently Solving Hamilton-Jacobi Equations](https://mlsanity.com/paper/2501.19351/) (2025)
- [Physics Informed Symbolic Networks](https://mlsanity.com/paper/2207.06240/) (2022)
- [Closed-form Solutions: A New Perspective on Solving Differential Equations](https://mlsanity.com/paper/2405.14620/) (2024)

## Built on by (most cited first, 1 of 1)

- [Enhancing Transformer Representations of Symbolic ODE Expressions](https://mlsanity.com/paper/2609.24746/) (2026)

## Abstract (arXiv)

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.