Mimicking the Physicist's Eye:A VLM-centric Approach for Physics Formula
  Discovery
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/
68b595ffdc94ad77a7bfcfbb
Jiaqi Liu
claimed_verified
2025-09-08T07:02:35.126Z
684ff37fa383bc5d6b0ff77f
https://cdn-avatars.huggingface.co/v1/production/uploads/no-auth/0JPr-cd_rxQz3k6rmzBOF.png
JiaqiLiu
user
JiaaqiLiu
68b595ffdc94ad77a7bfcfbc
Songning Lai
68b595ffdc94ad77a7bfcfbd
Pengze Li
68b595ffdc94ad77a7bfcfbe
Di Yu
68b595ffdc94ad77a7bfcfbf
Wenjie Zhou
68b595ffdc94ad77a7bfcfc0
Yiyang Zhou
68b595ffdc94ad77a7bfcfc1
Peng Xia
68b595ffdc94ad77a7bfcfc2
Zijun Wang
68b595ffdc94ad77a7bfcfc3
Xi Chen
68b595ffdc94ad77a7bfcfc4
Shixiang Tang
68b595ffdc94ad77a7bfcfc5
Lei Bai
68b595ffdc94ad77a7bfcfc6
Wanli Ouyang
68b595ffdc94ad77a7bfcfc7
Mingyu Ding
68b595ffdc94ad77a7bfcfc8
Huaxiu Yao
68b595ffdc94ad77a7bfcfc9
Aoran Wang
claimed_verified
2025-09-02T07:56:38.934Z
666839475ddf78d3bc5b80f4
https://cdn-avatars.huggingface.co/v1/production/uploads/noauth/j4OBskJ_GMS2QGE_nEuEJ.jpeg
Aoran Wang
user
RalfWang
Mimicking the Physicist's Eye:A VLM-centric Approach for Physics Formula
  Discovery
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/
VIPER-R1, a multimodal model combining visual perception, trajectory data, and symbolic reasoning, discovers physical laws with higher accuracy and interpretability than existing methods.
Visual Induction Physics-based Equation Reasoning Motion Structure Induction Causal Chain of Thought Reward-Guided Symbolic Calibration Symbolic Residual Realignment PhysSymbol multimodal model symbolic regression reinforcement learning