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.
@article{arxiv.2604.08863,
title = {Hidden in Plain Sight: Visual-to-Symbolic Analytical Solution Inference from Field Visualizations},
author = {Pengze Li and Jiaquan Zhang and Yunbo Long and Xinping Liu and Zhou wenjie and Encheng Su and Zihang Zeng and Jiaqi Liu and Jiyao Liu and Junchi Yu and Lihao Liu and Philip Torr and Shixiang Tang and Aoran Wang and Xi Chen},
journal= {arXiv preprint arXiv:2604.08863},
year = {2026}
}