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

Computer Science > Artificial Intelligence [Submitted on 10 Apr 2026] Hidden in Plain Sight: Visual-to-Symbolic Analytical Solution Inference from Field Visualizations 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 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. Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2604.08863 [cs.AI]   (or arXiv:2604.08863v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2604.08863 Focus to learn more Submission history From: Pengze Li [view email] [v1] Fri, 10 Apr 2026 01:52:02 UTC (749 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-04 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)