# Hidden in Plain Sight: Visual-to-Symbolic Analytical Solution Inference from Field Visualizations

arXiv: https://arxiv.org/abs/2604.08863 · HTML: https://mlsanity.com/paper/2604.08863/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 9 of its 41 references that are in the map.
- First posted on arXiv 10 Apr 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 9 of 9)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [MME: A Comprehensive Evaluation Benchmark for Multimodal Large Language Models](https://mlsanity.com/paper/2306.13394/) (2023)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [UGPhysics: A Comprehensive Benchmark for Undergraduate Physics Reasoning with Large Language Models](https://mlsanity.com/paper/2502.00334/) (2025)
- [PhysUniBench: A Multi-Modal Physics Reasoning Benchmark at Undergraduate Level](https://mlsanity.com/paper/2506.17667/) (2025)
- [S-Chain: Structured Visual Chain-of-Thought For Medicine](https://mlsanity.com/paper/2510.22728/) (2025)
- [Mimicking the Physicist's Eye:A VLM-centric Approach for Physics Formula Discovery](https://mlsanity.com/paper/2508.17380/) (2025)
- [SciIF: Benchmarking Scientific Instruction Following Towards Rigorous Scientific Intelligence](https://mlsanity.com/paper/2601.04770/) (2026)
- [ViSymRe: Vision Multimodal Symbolic Regression](https://mlsanity.com/paper/2412.11139/) (2024)

## Abstract (arXiv)

Recovering analytical solutions of physical fields from visual observations is a fundamental yet underexplored capability for AI-assisted scientific reasoning. We study visual-to-symbolic analytical solution inference (ViSA) for two-dimensional linear steady-state fields: given field visualizations (and first-order derivatives) plus minimal auxiliary metadata, the model must output a single executable SymPy expression with fully instantiated numeric constants. We introduce ViSA-R2 and align it with a self-verifying, solution-centric chain-of-thought pipeline that follows a physicist-like pathway: structural pattern recognition solution-family (ansatz) hypothesis parameter derivation consistency verification. We also release ViSA-Bench, a VLM-ready synthetic benchmark covering 30 linear steady-state scenarios with verifiable analytical/symbolic annotations, and evaluate predictions by numerical accuracy, expression-structure similarity, and character-level accuracy. Using an 8B open-weight Qwen3-VL backbone, ViSA-R2 outperforms strong open-source baselines and the evaluated closed-source frontier VLMs under a standardized protocol.