Al-Khwarizmi: Discovering Physical Laws with Foundation Models
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918065133846528 |
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| author | Mower, Christopher E. Bou-Ammar, Haitham |
| author_facet | Mower, Christopher E. Bou-Ammar, Haitham |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01702 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Al-Khwarizmi: Discovering Physical Laws with Foundation Models Mower, Christopher E. Bou-Ammar, Haitham Machine Learning 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. |
| title | Al-Khwarizmi: Discovering Physical Laws with Foundation Models |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2502.01702 |