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

TL;DR

This paper introduces VIPER-R1, a multimodal AI model that mimics physicists' visual reasoning to discover physical laws from observational data, outperforming existing methods in accuracy and interpretability.

Contribution

The paper presents VIPER-R1, a novel multimodal model integrating visual perception and symbolic reasoning for physics formula discovery, along with a new PhysSymbol dataset.

Findings

VIPER-R1 outperforms state-of-the-art VLMs in accuracy.

The model achieves better interpretability in physical law discovery.

PhysSymbol dataset supports multimodal physics research.

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/