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

TL;DR

This paper introduces ViSA, a model that infers analytical solutions from visualizations of physical fields, combining pattern recognition and verification, and provides a benchmark for evaluation.

Contribution

The paper presents ViSA-R2, a novel approach for visual-to-symbolic inference, and releases ViSA-Bench, a synthetic benchmark for evaluating such models.

Findings

ViSA-R2 outperforms open-source baselines in accuracy.

The benchmark covers 30 linear steady-state scenarios.

The approach aligns with physicist-like reasoning pathways.

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.