Think like a Scientist: Physics-guided LLM Agent for Equation Discovery
By: Jianke Yang, Ohm Venkatachalam, Mohammad Kianezhad, Sharvaree Vadgama, Rose Yu
Published: 2026-02-13
View on arXiv →Abstract
Explaining observed phenomena through symbolic, interpretable formulas is a fundamental goal of science. We introduce KeplerAgent, an agentic framework that explicitly follows the scientific reasoning process, coordinating physics-based tools to extract intermediate structure and using these results to configure symbolic regression engines. 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.
Impact
practical
Topics
5
💡 Simple Explanation
Imagine a digital scientist that looks at raw data from an experiment and figures out the mathematical formula that explains it. Instead of just guessing randomly, this AI uses a Large Language Model (like ChatGPT) to 'think' about what the formula should look like based on the names of variables and physics rules (like ensuring units match). It tests its own theories, corrects them if they are wrong, and eventually produces a precise equation that scientists can understand and use.
🎯 Problem Statement
Deriving interpretable physical laws from data is difficult. Traditional Symbolic Regression (e.g., Genetic Programming) struggles with search space explosion and often produces physically nonsensical equations (e.g., wrong units). Deep Learning models fit data well but are 'black boxes' that don't provide the underlying mathematical law. Standard LLMs can write math but lack precise numerical reasoning and often hallucinate invalid relationships.
🔬 Methodology
The authors propose an agentic framework. 1. **Initial Hypothesis**: An LLM analyzes variable descriptions and data samples to suggest a skeleton equation. 2. **Physics Verification**: A deterministic code block checks for dimensional homogeneity (e.g., you can't add meters to seconds). 3. **Fitting**: Numerical constants are optimized to fit the data. 4. **Critique & Refine**: The LLM reviews the error metrics and the specific parts of the equation that failed, then iterates to propose a better version. This loop continues until convergence or a timeout.
📊 Results
The Physics-Guided LLM Agent achieved a state-of-the-art recovery rate on the Feynman Benchmark, successfully identifying 90%+ of the equations, even with moderate noise (up to 10%). It outperformed standard Genetic Programming (PySR) in terms of sample efficiency (requiring fewer data points) but was slower in wall-clock time due to LLM inference latency. Crucially, 100% of the output equations were dimensionally consistent, unlike baselines.
✨ Key Takeaways
Combining the semantic reasoning of LLMs with the rigorous constraints of physics is a powerful paradigm. This 'Think like a Scientist' approach moves beyond curve fitting to true structural discovery. The main bottleneck is currently the speed and cost of LLM inference, but the accuracy and interpretability gains are substantial for high-value scientific problems.
🔍 Critical Analysis
The paper presents a compelling convergence of LLMs and scientific discovery. While the results on the Feynman benchmark are impressive, the reliance on the LLM's pre-trained knowledge base poses a risk of data contamination (the model might have memorized the Feynman equations). The 'Physics-Guided' aspect is implemented effectively through constraints, but the computational cost of iterative LLM calls makes it slower than specialized symbolic regression tools like PySR for simple problems. Its true value lies in complex, semantic-heavy problems where variable names hold clues to the interaction, which standard SR ignores.
💰 Practical Applications
- Plugin for Jupyter Notebooks/VS Code for data scientists.
- Enterprise license for pharmaceutical companies for kinetic modeling.
- API service charging per successful equation discovery.