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

Source: [Hidden in Plain Sight: Visual-to-Symbolic Analytical Solution Inference from Field Visualizations](<https://www.sota2.com/research/paper/69dc78997d0172140ec78bb4>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-04-14T05:00:04.234Z

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

Published: 2026-04-10T01:52:02.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Visual-to-Symbolic Analytical Solution Inference on ViSA-Bench VLM setting](<https://www.sota2.com/research/sota/visual-to-symbolic-analytical-solution-inference-on-visa-bench-vlm-setting.md>): Visual-to-Symbolic Analytical Solution Inference; ViSA-Bench VLM setting; Overall Accuracy: 51.2.

- [Visual-to-symbolic analytical solution inference on Visual-to-Symbolic Analytical Solution Inference](<https://www.sota2.com/research/sota/visual-to-symbolic-analytical-solution-inference-on-visual-to-symbolic-analytical-solution-inference.md>): Visual-to-Symbolic Analytical Solution Inference; Visual-to-Symbolic Analytical Solution Inference; Overall Score: 51.2.

- [Visual-to-Symbolic Analytical Solution Inference on ViSA-Bench LLM-only setting](<https://www.sota2.com/research/sota/visual-to-symbolic-analytical-solution-inference-on-visa-bench-llm-only-setting.md>): Visual-to-Symbolic Analytical Solution Inference; ViSA-Bench LLM-only setting; Overall Accuracy: not recorded.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2604.08863>)

[PDF](<https://arxiv.org/pdf/2604.08863.pdf>)