Inferring physical laws from data is a central challenge in science and engineering, including but not limited to healthcare, physical sciences, biosciences, social sciences, sustainability, climate, and robotics. Deep networks offer high-accuracy results but lack interpretability, prompting interest in models built from simple components. The Sparse Identification of Nonlinear Dynamics (SINDy) method has become the go-to approach for building such modular and interpretable models. SINDy leverages sparse regression with L1 regularization to identify key terms from a library of candidate functions. However, SINDy's choice of candidate library and optimization method requires significant technical expertise, limiting its widespread applicability. This work introduces Al-Khwarizmi, a novel agentic framework for physical law discovery from data, which integrates foundational models with SINDy. Leveraging LLMs, VLMs, and Retrieval-Augmented Generation (RAG), our approach automates physical law discovery, incorporating prior knowledge and iteratively refining candidate solutions via reflection. Al-Khwarizmi operates in two steps: it summarizes system observations-comprising textual descriptions, raw data, and plots-followed by a secondary step that generates candidate feature libraries and optimizer configurations to identify hidden physics laws correctly. Evaluating our algorithm on over 198 models, we demonstrate state-of-the-art performance compared to alternatives, reaching a 20 percent increase against the best-performing alternative.
View on arXiv@article{mower2025_2502.01702,
title={ Al-Khwarizmi: Discovering Physical Laws with Foundation Models },
author={ Christopher E. Mower and Haitham Bou-Ammar },
journal={arXiv preprint arXiv:2502.01702},
year={ 2025 }
}