arXiv 2602.073602026-02-07eess.SYcs.SY

基于大语言模型的非线性动力学在境系统识别

In-Context System Identification for Nonlinear Dynamics Using Large Language Models

Linyu Lin

备注：: 6 pages, 5 figures, submitted to The 10th IEEE Conference on Control Technology and Applications (CCTA) 2026

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AI总结：

本文提出一种利用大语言模型辅助SINDy的方法，通过在境学习迭代优化方程结构，提升复杂动力学系统的符号恢复精度与可解释性。

摘要：

稀疏识别非线性动力学（SINDy）是一种从数据中发现简洁控制方程的强大方法，但通常需要专家调整候选库。我们提出了一种由大语言模型（LLM）辅助的SINDy流程，通过在境学习迭代地使用大语言模型改进候选方程。该流程首先使用自适应库拟合一个基线SINDy模型，然后进入由LLM引导的细化循环。在每次迭代中，当前最佳方程、误差指标和领域特定约束都会被总结成提示，提交给LLM，以建议新的方程结构。这些候选方程会被解析到定义的符号形式，并在训练和测试数据上进行评估。该流程使用基于模拟的误差作为主要指标，但也评估与地面真相的结构相似性，包括匹配的功能形式、关键术语、耦合、定性行为。一个迭代停止准则会在测试误差低于阈值（NRMSE < 0.1）或达到最大10次迭代时提前结束细化。最后，最佳模型被选择，我们评估了这种由LLM辅助的SINDy在63个动态系统数据集（ODEBench）和march leuba模型（用于沸核反应堆）上的效果。结果与经典SINDy相比，LLM循环在复杂动力学情况下始终提高了符号恢复，具有更高的方程相似性与地面真相，以及更低的测试RMSE。这项工作表明，LLM可以有效地引导SINDy通过方程空间，整合数据驱动的误差反馈与领域启发的符号推理，以发现不仅准确而且结构可解释的控制方程。

英文摘要：

Sparse Identification of Nonlinear Dynamics (SINDy) is a powerful method for discovering parsimonious governing equations from data, but it often requires expert tuning of candidate libraries. We propose an LLM-aided SINDy pipeline that iteratively refines candidate equations using a large language model (LLM) in the loop through in-context learning. The pipeline begins with a baseline SINDy model fit using an adaptive library and then enters a LLM-guided refinement cycle. At each iteration, the current best equations, error metrics, and domain-specific constraints are summarized in a prompt to the LLM, which suggests new equation structures. These candidate equations are parsed against a defined symbolic form and evaluated on training and test data. The pipeline uses simulation-based error as a primary metric, but also assesses structural similarity to ground truth, including matching functional forms, key terms, couplings, qualitative behavior. An iterative stopping criterion ends refinement early if test error falls below a threshold (NRMSE < 0.1) or if a maximum of 10 iterations is reached. Finally, the best model is selected, and we evaluate this LLM-aided SINDy on 63 dynamical system datasets (ODEBench) and march leuba model for boiling nuclear reactor. The results are compared against classical SINDy and show the LLM-loop consistently improves symbolic recovery with higher equation similarity to ground truth and lower test RMSE than baseline SINDy for cases with complex dynamics. This work demonstrates that an LLM can effectively guide SINDy's search through equation space, integrating data-driven error feedback with domain-inspired symbolic reasoning to discover governing equations that are not only accurate but also structurally interpretable.

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