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This research addresses a critical bottleneck in AI-driven scientific discovery by introducing "data interpretation" to convert raw spatiotemporal fields into physical invariants suitable for Large Language Models. The method nearly triples the accuracy of recovered partial differential equations compared to using raw data, offering a scalable approach to automate theory construction without additional training costs. By bridging the gap between raw simulation outputs and human-readable physical quantities, this work advances the capability of LLMs to function as effective partners in molecular science and physics.
What Should a Large Language Model See? Physical Invariants as a Data Representation for PDE Discovery
arXiv:2608.25189v1 Announce Type: new 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.
Title:What Should a Large Language Model See? Physical Invariants as a Data Representation for PDE Discovery
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.
Machine Learning (cs.LG); Soft Condensed Matter (cond-mat.soft)
arXiv:2608.25189 [cs.LG]
(or arXiv:2608.25189v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2608.25189 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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