融合物理先验与深度学习，精准识别动态系统与参数。
Dynamics-Encoded Deep Learning for Robust System Identification and Parameter Estimation
- 将系统动力学信息嵌入深度网络架构中
- 在含噪观测下准确预测振荡与混沌系统行为
- 适合需要高鲁棒性建模的工程与科学场景
将先验物理知识融入机器学习可提升算法的鲁棒性与可解释性。本文结合深度学习与经典微分方程数值方法，解决动力系统理论中的两大挑战：动力学发现与参数估计。所提方法将已知的动力学信息编码至深度学习结构中，针对不同输入与输出假设进行设计。实验表明，在一系列包含振荡与混沌特性的测试问题上，该方法能有效应对污染观测数据，实现数据驱动的模型预测。对比多种数值方案（如Runge-Kutta与线性多步法），在合理选择空间与时间离散化方案及数值方法阶数时，系统动态预测与物理参数估计均取得优异结果。
原文摘要 · Abstract (English)
Incorporating a priori physics knowledge into machine learning leads to more robust and interpretable algorithms. In this work, we combine deep learning techniques and classic numerical methods for differential equations to address two challenging missing physics problems in dynamical systems theory: dynamics discovery and parameter estimation. The presented methods encode available information relating to the system dynamics into deep learning architectures, incorporating different assumptions on the known inputs and desired outputs in each case. Results demonstrate the effectiveness of the proposed approaches in making data-driven model predictions given corrupt system observations on a suite of test problems exhibiting oscillatory and chaotic dynamics. When comparing the performance of various numerical schemes, such as the Runge-Kutta and linear multistep families of methods, we observe promising results in predicting the system dynamics and estimating physical parameters, given appropriate choices of spatial and temporal discretization schemes and numerical method orders.
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