# Think like a Scientist: Physics-guided LLM Agent for Equation Discovery

arXiv: https://arxiv.org/abs/2602.12259 · HTML: https://mlsanity.com/paper/2602.12259/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 26 of its 40 references that are in the map.
- First posted on arXiv 12 Feb 2026.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)
- LLM agents and tool use / [Web, search, and research agents](https://mlsanity.com/agents/web-search-and-research-agents/)

## Builds on (most cited first, 26 of 26)

- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [Weak SINDy For Partial Differential Equations](https://mlsanity.com/paper/2007.02848/) (2020)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [PMLB: A Large Benchmark Suite for Machine Learning Evaluation and Comparison](https://mlsanity.com/paper/1703.00512/) (2017)
- [Extrapolation and learning equations](https://mlsanity.com/paper/1610.02995/) (2016)
- [PySINDy: A comprehensive Python package for robust sparse system identification](https://mlsanity.com/paper/2111.08481/) (2021)
- [Symbolic Regression with a Learned Concept Library](https://mlsanity.com/paper/2409.09359/) (2024)
- [LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models](https://mlsanity.com/paper/2504.10415/) (2025)
- [Generative Adversarial Symmetry Discovery](https://mlsanity.com/paper/2302.00236/) (2023)
- [SR-Scientist: Scientific Equation Discovery With Agentic AI](https://mlsanity.com/paper/2510.11661/) (2025)
- [In-Context Symbolic Regression: Leveraging Large Language Models for Function Discovery](https://mlsanity.com/paper/2404.19094/) (2024)
- [Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling](https://mlsanity.com/paper/2109.05364/) (2021)
- [Dimensionally Consistent Learning with Buckingham Pi](https://mlsanity.com/paper/2202.04643/) (2022)
- [Learning Infinitesimal Generators of Continuous Symmetries from Data](https://mlsanity.com/paper/2410.21853/) (2024)
- [Symmetry-Informed Governing Equation Discovery](https://mlsanity.com/paper/2405.16756/) (2024)
- [Tool-to-Agent Retrieval: Bridging Tools and Agents for Scalable LLM Multi-Agent Systems](https://mlsanity.com/paper/2511.01854/) (2025)
- [Coarse-Graining Hamiltonian Systems Using WSINDy](https://mlsanity.com/paper/2310.05879/) (2023)
- [In Context Learning and Reasoning for Symbolic Regression with Large Language Models](https://mlsanity.com/paper/2410.17448/) (2024)
- [Discovering Symbolic Differential Equations with Symmetry Invariants](https://mlsanity.com/paper/2505.12083/) (2025)

## Built on by (most cited first, 16 of 16)

- [DiscoverPhysics: Benchmarking LLMs for Out-of-the-Box Scientific Thinking](https://mlsanity.com/paper/2605.26087/) (2026)
- [MaD Physics: Evaluating information seeking under constraints in physical environments](https://mlsanity.com/paper/2605.10820/) (2026)
- [STRIDE: A Self-Reflective Agent Framework for Reliable Automatic Equation Discovery](https://mlsanity.com/paper/2605.17790/) (2026)
- [Toward Evaluation Frameworks for Multi-Agent Scientific AI Systems](https://mlsanity.com/paper/2603.26718/) (2026)
- [Discovery of Interpretable Surrogates via Agentic AI: Application to Gravitational Waves](https://mlsanity.com/paper/2605.11280/) (2026)
- [MechBench: Can AI Scientific Agents Discover Mechanisms Beyond Phenomenal Laws?](https://mlsanity.com/paper/2609.35515/) (2026)
- [LLM-driven design of physics-constrained constitutive models: two agents are better than one](https://mlsanity.com/paper/2605.23754/) (2026)
- [LLM-Guided ODE Discovery and Parameter Inference from Small-Cohort Aggregate Data](https://mlsanity.com/paper/2607.00733/) (2026)
- [On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement](https://mlsanity.com/paper/2607.23753/) (2026)
- [Large language models for partial differential equation workflows](https://mlsanity.com/paper/2608.03600/) (2026)
- [See, Hypothesize, Validate: Multimodal Agentic Framework for Discovering Governing PDEs](https://mlsanity.com/paper/2608.27869/) (2026)
- [Collaborative Principle Evolution via Evidence Transfer for Scientific Discovery](https://mlsanity.com/paper/2609.35315/) (2026)
- [SRHarness: A Harness for Agentic Symbolic Regression](https://mlsanity.com/paper/2609.35501/) (2026)
- [How AI Agents Discover Scientific Equations: From Hydrotope Rediscovery to New Water-Wave Amplitudes](https://mlsanity.com/paper/2610.00435/) (2026)
- [Learning to Design SR Solvers: Harness Optimization for Symbolic Regression](https://mlsanity.com/paper/2610.16966/) (2026)
- [Coupled Harness--Model Evolution for Scientific Equation Discovery](https://mlsanity.com/paper/2610.17740/) (2026)

## Abstract (arXiv)

Explaining observed phenomena through symbolic, interpretable formulas is a fundamental goal of science. Recently, large language models (LLMs) have emerged as promising tools for symbolic equation discovery, owing to their broad domain knowledge and strong reasoning capabilities. However, most existing LLM-based systems try to guess equations directly from data, without modeling the multi-step reasoning process that scientists often follow: first inferring physical properties such as symmetries, then using these as priors to restrict the space of candidate equations. We introduce KeplerAgent, an agentic framework that explicitly follows this scientific reasoning process. The agent coordinates physics-based tools to extract intermediate structure and uses these results to configure symbolic regression engines such as PySINDy and PySR, including their function libraries and structural constraints. Across a suite of physical equation benchmarks, KeplerAgent achieves substantially higher symbolic accuracy and greater robustness to noisy data than both LLM and traditional baselines.