[2604.08863] Hidden in Plain Sight: Visual-to-Symbolic Analytical Solution Inference from Field Visualizations

Computer Science > Artificial Intelligence arXiv:2604.08863 (cs) [Submitted on 10 Apr 2026] Title:Hidden in Plain Sight: Visual-to-Symbolic Analytical Solution Inference from Field Visualizations Authors:Pengze Li, Jiaquan Zhang, Yunbo Long, Xinping Liu, Zhou wenjie, Encheng Su, Zihang Zeng, Jiaqi Liu, Jiyao Liu, Junchi Yu, Lihao Liu, Philip Torr, Shixiang Tang, Aoran Wang, Xi Chen View a PDF of the paper titled Hidden in Plain Sight: Visual-to-Symbolic Analytical Solution Inference from Field Visualizations, by Pengze Li and 14 other authors View PDF HTML (experimental) Abstract: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 acc...