Mimicking the Physicist's Eye:A VLM-centric Approach for Physics Formula Discovery

• URL: http://arxiv.org/abs/2508.17380v1
• Date: Sun, 24 Aug 2025 14:34:21 GMT
• Title: Mimicking the Physicist's Eye:A VLM-centric Approach for Physics Formula Discovery
• Authors: Jiaqi Liu, Songning Lai, Pengze Li, Di Yu, Wenjie Zhou, Yiyang Zhou, Peng Xia, Zijun Wang, Xi Chen, Shixiang Tang, Lei Bai, Wanli Ouyang, Mingyu Ding, Huaxiu Yao, Aoran Wang,
• Abstract summary: VIPERR-aq1 is a multimodal model that performs Visual Induction for Equation Reasoning.<n>It integrates visual perception, trajectory data, and symbolic reasoning to emulate the scientific discovery process.<n>It consistently outperforms state-of-the-art VLM baselines in accuracy and interpretability.
• Score: 98.58830663687911
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Automated discovery of physical laws from observational data in the real world is a grand challenge in AI. Current methods, relying on symbolic regression or LLMs, are limited to uni-modal data and overlook the rich, visual phenomenological representations of motion that are indispensable to physicists. This "sensory deprivation" severely weakens their ability to interpret the inherent spatio-temporal patterns within dynamic phenomena. To address this gap, we propose VIPER-R1, a multimodal model that performs Visual Induction for Physics-based Equation Reasoning to discover fundamental symbolic formulas. It integrates visual perception, trajectory data, and symbolic reasoning to emulate the scientific discovery process. The model is trained via a curriculum of Motion Structure Induction (MSI), using supervised fine-tuning to interpret kinematic phase portraits and to construct hypotheses guided by a Causal Chain of Thought (C-CoT), followed by Reward-Guided Symbolic Calibration (RGSC) to refine the formula structure with reinforcement learning. During inference, the trained VIPER-R1 acts as an agent: it first posits a high-confidence symbolic ansatz, then proactively invokes an external symbolic regression tool to perform Symbolic Residual Realignment (SR^2). This final step, analogous to a physicist's perturbation analysis, reconciles the theoretical model with empirical data. To support this research, we introduce PhysSymbol, a new 5,000-instance multimodal corpus. Experiments show that VIPER-R1 consistently outperforms state-of-the-art VLM baselines in accuracy and interpretability, enabling more precise discovery of physical laws. Project page: https://jiaaqiliu.github.io/VIPER-R1/

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