Discovery of Interpretable Physical Laws in Materials via Language-Model-Guided Symbolic Regression

2026-02-26

AI Summary

This work addresses the challenge that traditional symbolic regression often yields overly complex and physically meaningless expressions when applied to high-dimensional materials data. To overcome this limitation, the authors propose a novel approach that, for the first time, integrates large language models (LLMs) into the symbolic regression pipeline. By leveraging the embedded scientific knowledge within LLMs to guide the search direction and combining it with combinatorial optimization-based pruning techniques, the method substantially reduces the solution space while ensuring the physical interpretability of the resulting formulas. The approach efficiently discovers new analytical expressions for key material properties—including perovskite bulk modulus, bandgap, and oxygen evolution reaction activity—that consistently outperform existing results in terms of accuracy, simplicity, and physical plausibility.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Search and Retrieval-Augmented AI: Large language models for search
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Discovering interpretable physical laws from high-dimensional data is a fundamental challenge in scientific research. Traditional methods, such as symbolic regression, often produce complex, unphysical formulas when searching a vast space of possible forms. We introduce a framework that guides the search process by leveraging the embedded scientific knowledge of large language models, enabling efficient identification of physical laws in the data. We validate our approach by modeling key properties of perovskite materials. Our method mitigates the combinatorial explosion commonly encountered in traditional symbolic regression, reducing the effective search space by a factor of approximately $10^5$. A set of novel formulas for bulk modulus, band gap, and oxygen evolution reaction activity are identified, which not only provide meaningful physical insights but also outperform previous formulas in accuracy and simplicity.

Problem

• symbolic regression
• interpretable physical laws
• high-dimensional data
• materials science
• combinatorial explosion

Innovation

• language-model-guided symbolic regression
• interpretable physical laws
• perovskite materials
• combinatorial explosion mitigation
• scientific discovery