# StruSR: Structure-Aware Symbolic Regression with Physics-Informed Taylor Guidance

arXiv: https://arxiv.org/abs/2510.06635 · HTML: https://mlsanity.com/paper/2510.06635/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 41 references that are in the map.
- First posted on arXiv 8 Oct 2025.

## Builds on (most cited first, 21 of 21)

- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems](https://mlsanity.com/paper/1710.00211/) (2017)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction](https://mlsanity.com/paper/1704.02971/) (2017)
- [Time Series Data Augmentation for Deep Learning: A Survey](https://mlsanity.com/paper/2002.12478/) (2020)
- [A Deep Neural Network for Unsupervised Anomaly Detection and Diagnosis in Multivariate Time Series Data](https://mlsanity.com/paper/1811.08055/) (2018)
- [Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretability](https://mlsanity.com/paper/2406.02496/) (2024)
- [Person Re-identification Method Based on Color Attack and Joint Defence](https://mlsanity.com/paper/2111.09571/) (2021)
- [Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws](https://mlsanity.com/paper/2303.03192/) (2023)
- [Eliminate Deviation with Deviation for Data Augmentation and a General Multi-modal Data Learning Method](https://mlsanity.com/paper/2101.08533/) (2021)
- [Out-of-Distribution Representation Learning for Time Series Classification](https://mlsanity.com/paper/2209.07027/) (2022)
- [GP-Tree: A Gaussian Process Classifier for Few-Shot Incremental Learning](https://mlsanity.com/paper/2102.07868/) (2021)
- [Beyond Augmentation: Empowering Model Robustness under Extreme Capture Environments](https://mlsanity.com/paper/2407.13640/) (2024)
- [Phy124: Fast Physics-Driven 4D Content Generation from a Single Image](https://mlsanity.com/paper/2409.07179/) (2024)
- [Taylor Genetic Programming for Symbolic Regression](https://mlsanity.com/paper/2205.09751/) (2022)
- [Beyond Dropout: Robust Convolutional Neural Networks Based on Local Feature Masking](https://mlsanity.com/paper/2407.13646/) (2024)
- [Adversarial Learning for Neural PDE Solvers with Sparse Data](https://mlsanity.com/paper/2409.02431/) (2024)
- [Cross-Modality Attack Boosted by Gradient-Evolutionary Multiform Optimization](https://mlsanity.com/paper/2409.17977/) (2024)
- [Cross-Task Attack: A Self-Supervision Generative Framework Based on Attention Shift](https://mlsanity.com/paper/2407.13700/) (2024)
- [Symbolic Regression for PDEs using Pruned Differentiable Programs](https://mlsanity.com/paper/2303.07009/) (2023)

## Built on by (most cited first, 6 of 6)

- [Diffusion-Based Image Editing: An Unforeseen Adversary to Robust Invisible Watermarks](https://mlsanity.com/paper/2511.05598/) (2025)
- [Vanishing Watermarks: Diffusion-Based Image Editing Undermines Robust Invisible Watermarking](https://mlsanity.com/paper/2602.20680/) (2026)
- [Editing on the Generative Manifold: A Theoretical and Empirical Study of General Diffusion-Based Image Editing Trade-offs](https://mlsanity.com/paper/2603.29736/) (2026)
- [When Denoising Becomes Unsigning: Theoretical and Empirical Analysis of Watermark Fragility Under Diffusion-Based Image Editing](https://mlsanity.com/paper/2603.04696/) (2026)
- [Editing Away the Evidence: Diffusion-Based Image Manipulation and the Failure Modes of Robust Watermarking](https://mlsanity.com/paper/2603.12949/) (2026)
- [DeSyR: A Decoupled Symbolic Recovery Framework with PINN-Guided Structure Search and Physics-Informed Coefficient Refinement](https://mlsanity.com/paper/2609.00530/) (2026)

## Abstract (arXiv)

Symbolic regression aims to find interpretable analytical expressions by searching over mathematical formula spaces to capture underlying system behavior, particularly in scientific modeling governed by physical laws. However, traditional methods lack mechanisms for extracting structured physical priors from time series observations, making it difficult to capture symbolic expressions that reflect the system's global behavior. In this work, we propose a structure-aware symbolic regression framework, called StruSR, that leverages trained Physics-Informed Neural Networks (PINNs) to extract locally structured physical priors from time series data. By performing local Taylor expansions on the outputs of the trained PINN, we obtain derivative-based structural information to guide symbolic expression evolution. To assess the importance of expression components, we introduce a masking-based attribution mechanism that quantifies each subtree's contribution to structural alignment and physical residual reduction. These sensitivity scores steer mutation and crossover operations within genetic programming, preserving substructures with high physical or structural significance while selectively modifying less informative components. A hybrid fitness function jointly minimizes physics residuals and Taylor coefficient mismatch, ensuring consistency with both the governing equations and the local analytical behavior encoded by the PINN. Experiments on benchmark PDE systems demonstrate that StruSR improves convergence speed, structural fidelity, and expression interpretability compared to conventional baselines, offering a principled paradigm for physics-grounded symbolic discovery.