标题： 基于共形预测的非线性动力学稀疏识别 显示英文标题

标题： Sparse Identification of Nonlinear Dynamics with Conformal Prediction

摘要： 稀疏非线性动力学识别（SINDy）是一种从数据中发现非线性动力系统模型的方法。 在安全关键应用中，量化SINDy模型的不确定性对于评估其可靠性至关重要。 虽然存在各种用于SINDy的不确定性量化方法，包括贝叶斯和集合方法，但本文探讨了将符合预测（Conformal Prediction）整合进来，这是一种可以在最小假设（如数据可交换性）基础上提供有效预测区间并具有覆盖保证的框架。 我们介绍了与集合SINDy（E-SINDy）结合的符合预测的三个应用：（1）量化时间序列预测的不确定性，（2）基于库特征重要性的模型选择，以及（3）使用特征符合预测量化识别模型系数的不确定性。 我们在随机捕食者-被捕食者动力学和几个混沌动力系统上展示了这三个应用。 我们表明，与E-SINDy结合的符合预测方法可以可靠地实现时间序列预测的目标覆盖，有效地量化特征重要性，并在非高斯噪声下相比标准E-SINDy系数估计产生更稳健的不确定性区间。 显示英文摘要

摘要： The Sparse Identification of Nonlinear Dynamics (SINDy) is a method for discovering nonlinear dynamical system models from data. Quantifying uncertainty in SINDy models is essential for assessing their reliability, particularly in safety-critical applications. While various uncertainty quantification methods exist for SINDy, including Bayesian and ensemble approaches, this work explores the integration of Conformal Prediction, a framework that can provide valid prediction intervals with coverage guarantees based on minimal assumptions like data exchangeability. We introduce three applications of conformal prediction with Ensemble-SINDy (E-SINDy): (1) quantifying uncertainty in time series prediction, (2) model selection based on library feature importance, and (3) quantifying the uncertainty of identified model coefficients using feature conformal prediction. We demonstrate the three applications on stochastic predator-prey dynamics and several chaotic dynamical systems. We show that conformal prediction methods integrated with E-SINDy can reliably achieve desired target coverage for time series forecasting, effectively quantify feature importance, and produce more robust uncertainty intervals for model coefficients, even under non-Gaussian noise, compared to standard E-SINDy coefficient estimates.