LLMs Discover PDEs Using Physical Invariants as Data Input

A major challenge in molecular sciences is bridging molecular interactions to macroscopic behaviors, a task where traditional theory building struggles to keep pace with vast modern datasets. Large Language Models (LLMs) offer a promising avenue for automating theory construction, but directly inputting raw spatiotemporal field data into an LLM prompt is not effective. Current LLMs typically learn about data only through a score indicating how well a proposed equation fits. This paper introduces a novel "data interpretation" stage. Instead of raw data, this stage measures the field into physically meaningful quantities, such as invariants, that a human theorist would consult. These interpreted quantities are then supplied directly to the LLM as input. On a benchmark of simulated fields, this interpretation method dramatically improves the accuracy of discovered Partial Differential Equations (PDEs), nearly tripling it compared to feeding raw data, all without any additional model training. This approach enables LLMs to "read" field data in a manner analogous to a human theorist, opening a practical path for automated field theory construction that can evolve alongside experimental data.