A Multi-agent Framework for Physical Laws Discovery

TL;DR

An LLM-based multi-agent framework for physical-law discovery that integrates literature-guided variable selection, hypothesis formulation, symbolic regression, formula derivation, and mechanistic explanation is developed, demonstrating that AI can increasingly serve as an essential role in modern scientific research by thinking and acting like field experts.

Abstract

Discovering explicit physical laws has traditionally depended on human intuition and domain expertise. Recent advances in artificial intelligence, particularly large language models (LLMs), offer a new route to accelerate this process by automating key steps from hypothesis generation to interpretable model construction. Here we develop an LLM-based multi-agent framework for physical-law discovery that integrates literature-guided variable selection, hypothesis formulation, symbolic regression, formula derivation, and mechanistic explanation. We validate the framework on three representative materials problems: the glass-forming ability (GFA) of metallic glasses, the Vickers hardness of compounds, and the Young's modulus of multi-component alloys. Using physically and chemically meaningful descriptors as inputs, the discovered formulas achieve strong agreement with reference data, with correlation coefficients up to 0.94 (GFA), 0.86 (hardness), and 0.94 (Young's modulus), while remaining compact and interpretable. Beyond fitting, the Young's modulus formula generalizes to quaternary and quinary alloys, improving prediction accuracy by up to 78.8% relative to the classical rule of mixtures. By integrating cross-disciplinary knowledge, reflection mechanisms, and expert-like reasoning ability into symbolic regression, our AI-centric framework offers a robust and extensible platform for automated physical laws discovery, demonstrating that AI can increasingly serve as an essential role in modern scientific research by thinking and acting like field experts.

Figures (3)

• Figure 1: Schematic of the proposed multi-agent framework for physical-law discovery. (a) A reasoning LLM conducts literature review and supports data preparation. (b) Multi-agent collaboration for proposing, evaluating, and refining candidate formulas with trajectory-based feedback. (c) Beam search balances predictive accuracy and expression complexity by retaining the top-$K$ candidates at each depth. (d) An explanation agent with RAG contextualizes and interprets the discovered formulas.
• Figure 2: Evolution trajectory of the best-discovered formula for the hardness prediction task. Using the stored derivation history in the memory module, the agents iteratively propose hypotheses and refine the expression across search depths. The left panel summarizes, at each depth, the structural changes to the formula together with the associated rationale, whereas the arrow on the right highlights the corresponding score improvements (lower is better).
• Figure 3: Comparison of Young's modulus predictions for the quaternary alloy $\text{Mo}_{25}\text{Ta}_{x}\text{Nb}_{y}\text{W}_{z}$ using DFT, the foundation atomic model DPA-3.1-3M, the proposed closed-form formula, and the law of mixtures (LoM). (a) Schematic workflow comparison from top to bottom: DFT, DPA-3.1-3M, proposed formula, and LoM. The last two columns report the predicted modulus for the representative alloy $\text{Mo}_{25}\text{Nb}_{15}\text{Ta}_{35}\text{W}_{25}$ and the corresponding computational cost, highlighting the favorable accuracy-efficiency trade-off of the proposed formula. (b) DPA-3.1-3M-predicted modulus map over the composition space. (c) Modulus map predicted by the proposed formula. (d) Modulus map predicted by LoM. (e) Accuracy versus computational cost for three representative compositions: Mo$_{25}$Nb$_5$W$_{25}$Ta$_{45}$, Mo$_{25}$Nb$_{15}$W$_{25}$Ta$_{35}$, and Mo$_{25}$Nb$_{25}$W$_{25}$Ta$_{25}$; DFT is taken as the reference (zero relative error). (f) Distribution of mean absolute percentage error (MAPE) of the proposed formula relative to DPA-3.1-3M across the sampled compositions. (g) MAPE distribution of LoM relative to DPA-3.1-3M.