用可验证的置信区间提升非线性系统建模的可靠性
Sparse Identification of Nonlinear Dynamics with Conformal Prediction
- 将共形预测融入集成SINDy，实现低假设下的不确定性量化
- 在混沌系统和随机捕食者-猎物模型中达成目标覆盖率
- 适合需要可信预测的工程与安全关键场景
稀疏识别非线性动力学（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模型的不确定性对评估其可靠性至关重要。尽管已有贝叶斯和集成等不确定性量化方法，本文探索将共形预测框架引入SINDy，该框架仅基于数据可交换性等最小假设即可提供具有覆盖率保证的预测区间。我们提出三种共形预测与集成SINDy（E-SINDy）结合的应用：(1) 时间序列预测的不确定性量化，(2) 基于库特征重要性的模型选择，(3) 使用特征共形预测量化识别模型系数的不确定性。我们在随机捕食者-猎物动力学及多个混沌系统上进行了验证。结果表明，融合共形预测的E-SINDy能可靠实现目标覆盖率，有效量化特征重要性，并在非高斯噪声下生成比标准E-SINDy更稳健的系数置信区间。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。