Mimicking the Physicist's Eye:A VLM-centric Approach for Physics Formula
  Discovery
Authors: name: Jiaqi Liu, name: Songning Lai, name: Pengze Li, name: Di Yu, name: Wenjie Zhou, name: Yiyang Zhou, name: Peng Xia, name: Zijun Wang, name: Xi Chen, name: Shixiang Tang, name: Lei Bai, name: Wanli Ouyang, name: Mingyu Ding, name: Huaxiu Yao, name: Aoran Wang

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/