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

arXiv: https://arxiv.org/abs/2508.17380 · HTML: https://mlsanity.com/paper/2508.17380/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 48 references that are in the map.
- First posted on arXiv 24 Aug 2025.

## Builds on (most cited first, 30 of 35)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [Qwen-VL: A Versatile Vision-Language Model for Understanding, Localization, Text Reading, and Beyond](https://mlsanity.com/paper/2308.12966/) (2023)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [The AI Scientist: Towards Fully Automated Open-Ended Scientific Discovery](https://mlsanity.com/paper/2408.06292/) (2024)
- [Vision-Language Models for Vision Tasks: A Survey](https://mlsanity.com/paper/2304.00685/) (2023)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Reasoning or Reciting? Exploring the Capabilities and Limitations of Language Models Through Counterfactual Tasks](https://mlsanity.com/paper/2307.02477/) (2023)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [Thinking with Images for Multimodal Reasoning: Foundations, Methods, and Future Frontiers](https://mlsanity.com/paper/2506.23918/) (2025)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [SciMON: Scientific Inspiration Machines Optimized for Novelty](https://mlsanity.com/paper/2305.14259/) (2023)
- [Evolution through Large Models](https://mlsanity.com/paper/2206.08896/) (2022)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [Hypothesis Search: Inductive Reasoning with Language Models](https://mlsanity.com/paper/2309.05660/) (2023)
- [DiscoveryBench: Towards Data-Driven Discovery with Large Language Models](https://mlsanity.com/paper/2407.01725/) (2024)
- [A Comprehensive Survey of Scientific Large Language Models and Their Applications in Scientific Discovery](https://mlsanity.com/paper/2406.10833/) (2024)
- [LLM and Simulation as Bilevel Optimizers: A New Paradigm to Advance Physical Scientific Discovery](https://mlsanity.com/paper/2405.09783/) (2024)
- [Symbolic Regression with a Learned Concept Library](https://mlsanity.com/paper/2409.09359/) (2024)
- [Can GPT-4 Perform Neural Architecture Search?](https://mlsanity.com/paper/2304.10970/) (2023)
- [Symbolic Regression is NP-hard](https://mlsanity.com/paper/2207.01018/) (2022)
- [LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models](https://mlsanity.com/paper/2504.10415/) (2025)
- [Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search](https://mlsanity.com/paper/2205.13134/) (2022)
- [Large Language Models As Evolution Strategies](https://mlsanity.com/paper/2402.18381/) (2024)
- [SNIP: Bridging Mathematical Symbolic and Numeric Realms with Unified Pre-training](https://mlsanity.com/paper/2310.02227/) (2023)
- [Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discovery](https://mlsanity.com/paper/2206.10540/) (2022)
- [Large Language Models are Zero Shot Hypothesis Proposers](https://mlsanity.com/paper/2311.05965/) (2023)

## Built on by (most cited first, 7 of 7)

- [NewtonBench: Benchmarking Generalizable Scientific Law Discovery in LLM Agents](https://mlsanity.com/paper/2510.07172/) (2025)
- [Agent0-VL: Exploring Self-Evolving Agent for Tool-Integrated Vision-Language Reasoning](https://mlsanity.com/paper/2511.19900/) (2025)
- [IRIS: A Real-World Benchmark for Inverse Recovery and Identification of Physical Dynamic Systems from Monocular Video](https://mlsanity.com/paper/2603.16432/) (2026)
- [CircuitSense: A Hierarchical MLLM Benchmark Bridging Visual Comprehension and Symbolic Reasoning in Engineering Design Process](https://mlsanity.com/paper/2509.22339/) (2025)
- [MATRIX: A Multimodal Benchmark and Post-Training Framework for Materials Science](https://mlsanity.com/paper/2602.00376/) (2026)
- [Scaling Participation in Modular AI Systems](https://mlsanity.com/paper/2606.07812/) (2026)
- [Hidden in Plain Sight: Visual-to-Symbolic Analytical Solution Inference from Field Visualizations](https://mlsanity.com/paper/2604.08863/) (2026)

## Abstract (arXiv)

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/