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

• URL: http://arxiv.org/abs/2604.08863v1
• Date: Fri, 10 Apr 2026 01:52:02 GMT
• Title: Hidden in Plain Sight: Visual-to-Symbolic Analytical Solution Inference from Field Visualizations
• Abstract summary: We study visual-to-symbolic analytical solution inference (ViSA) for two-dimensional linear steady-state fields.<n>We introduce ViSA-R2 and align it with a self-verifying, solution-centric chain-of-thought pipeline.<n>We also release ViSA-Bench, a VLM-ready synthetic benchmark covering 30 linear steady-state scenarios.
• Score: 37.91491674261653
• License: http://creativecommons.org/licenses/by/4.0/
• 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 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.

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