观测、假设、验证：用于发现控制偏微分方程的多模态智能体框架
See, Hypothesize, Validate: Multimodal Agentic Framework for Discovering Governing PDEs
- Indian Institute of Technology Delhi（印度德里理工学院）
- Robert Bosch GmbH（罗伯特·博世有限公司）
- TCS Research（塔塔咨询服务公司研究院）
- Yardi School of Artificial Intelligence (ScAI)（亚迪人工智能学院）
- Department of Applied Mechanics（应用力学系）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出多模态智能体框架MAGE，通过四个专业化智能体协作迭代发现控制PDE，在经典PDE套件等测试中实现优异恢复与误差表现，支持无库控制定律发现的结构化智能体推理研究。
AI中文摘要：
从观测数据中发现控制偏微分方程（PDE）仍是各学科面临的核心挑战。现有稀疏回归、符号回归及基于大语言模型（LLM）的方法，受限于预定义库、噪声敏感性、幻觉或有限的迭代优化。我们提出MAGE（Multimodal Agentic Governing Equation Discovery，多模态智能体控制方程发现），一种将PDE发现组织为置信度控制的假设验证循环的智能体框架，其灵感来自观察、假设与证伪的科学循环。四个角色专业化的智能体协同工作：计算导数与诊断可视化的微分观测器；由视觉语言模型（VLM）驱动的现象提取器，从多模态诊断中提炼定性线索；由LLM驱动的控制定律合成器，无需预定义库即可提出候选方程；以及方程仲裁器，用于拟合系数并分配置信度分数。发现过程迭代进行，直到最优候选方程达到用户指定的阈值，提供带有明确接受-拒绝协议的结构化流程。在评估的经典PDE套件上，MAGE实现了8/8的精确结构恢复，在7/8的系统中获得了对比方法中最低的系数误差，改进幅度最高达4个数量级，几何平均改进约为3个数量级。该流程还在两种复杂几何中恢复了预期算子，在一份实验室传感器记录上，选择了立方恢复力模型，其保留数据的决定系数R²=0.98538。这些结果支持进一步研究用于无库控制定律发现的结构化智能体推理，不过更广泛的泛化性仍有待评估。
英文摘要：
Discovering governing partial differential equations (PDEs) from observational data remains a core challenge across the sciences. Existing sparse-regression, symbolic-regression, and LLM-based approaches can be constrained by predefined libraries, noise sensitivity, hallucination, or limited iterative refinement. We introduce \textbf{MAGE} (\textbf{M}ultimodal \textbf{A}gentic \textbf{G}overning \textbf{E}quation Discovery), an agentic framework that organizes PDE discovery as a \textit{confidence governed hypothesis validation loop} inspired by the scientific cycle of observation, hypothesis, and falsification. Four role-specialized agents collaborate: a \textit{Differential Observer} computing derivatives and diagnostic visualizations; a VLM-powered \textit{Phenomenology Extractor} distilling qualitative cues from multimodal diagnostics; an LLM-driven \textit{Governing Law Synthesizer} proposing candidates without a predefined library; and an \textit{Equation Arbiter} fitting coefficients and assigning confidence scores. Discovery iterates until the top candidate clears a user-specified threshold, providing a structured process with an explicit accept-reject protocol. On the evaluated canonical PDE suite, MAGE obtains \textbf{8/8} exact structural recovery and the lowest coefficient error among the compared methods on \textbf{7/8} systems, with improvements of up to \textbf{4 orders of magnitude} and a geometric-mean improvement of approximately \textbf{3 orders of magnitude}. The pipeline also recovers the expected operators in two complex geometries and, on one laboratory sensor record, selects a cubic restoring-force model with held-out $R^2=0.98538$. These results support further study of structured agentic reasoning for library-free governing-law discovery, while broader generalization remains to be evaluated.
