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

arXiv: https://arxiv.org/abs/2608.25189 · HTML: https://mlsanity.com/paper/2608.25189/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 9 references that are in the map.
- First posted on arXiv 25 Aug 2026.

## Builds on (most cited first, 6 of 6)

- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [Symbolic Regression with a Learned Concept Library](https://mlsanity.com/paper/2409.09359/) (2024)
- [DrSR: LLM based Scientific Equation Discovery with Dual Reasoning from Data and Experience](https://mlsanity.com/paper/2506.04282/) (2025)
- [Influence-Guided Symbolic Regression: Scientific Discovery via LLM-Driven Equation Search with Granular Feedback](https://mlsanity.com/paper/2605.29184/) (2026)
- [LLM-ACES: Closed-Loop Discovery of Dynamical Systems with LLM-Guided Adaptive Search](https://mlsanity.com/paper/2606.25039/) (2026)
- [From Residuals to Reasons: LLM-Guided Mechanism Inference from Tabular Data](https://mlsanity.com/paper/2605.22897/) (2026)

## Abstract (arXiv)

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.