What Should a Large Language Model See? Physical Invariants as a Data Representation for PDE Discovery

2026-08-25

AI Summary

本文通过引入数据解释阶段，使大型语言模型能够像理论学家一样解读场数据，从而提高从实验数据中自动构建场理论的准确性。

Abstract

Understanding how molecular interactions govern macroscopic behaviour is a central challenge in molecular sciences. However, conventional theory building cannot keep pace with the vast datasets modern experimentation routinely produces. Large language models offer a promising route to automating theory construction, but a spatiotemporal field cannot be directly placed in a prompt. Existing models generally learn about the data only through a score measuring how well each proposal fits it. Here we introduce data interpretation, a stage that measures the field into the quantities a theorist would consult and supplies them to the model as a direct input. On a benchmark of simulated fields, interpretation nearly triples the accuracy of recovered equations relative to showing the raw data, at negligible computational cost and without any training. By allowing a language model to read field data as a theorist does, data interpretation offers a practical route to automated field theory construction that can coevolve with experimentation.

Problem

• molecular interactions
• macroscopic behaviour
• theory building
• large datasets
• experimentation

Innovation

• data interpretation
• large language models
• PDE discovery
• theory construction
• spatiotemporal field