基于RTS平滑器引导的物理神经网络微分模型学习
RTS Smoother-Guided Learning of Physics-Based Neural Differential Models
- Northeastern University（东北大学）
- University of Massachusetts Boston（马萨诸塞大学波士顿分校）
- Emory University（埃默里大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对部分状态变量可测、动力学方程部分未知的情况，提出混合神经-物理框架，交替进行状态和参数估计，利用RTS平滑器和反向传播，能从测量中学习缺失的ODE组件，提升潜在状态重建和长期预测能力。
AI中文摘要：
常微分方程（ODEs）广泛用于物理、生物、神经科学和生理学中的动力系统建模，但在许多应用中，动力学的一些方程未知，只有部分状态变量可测量。我们提出了一种混合神经-物理框架，其中ODE的已知部分保持显式，缺失部分由神经网络表示。该方法包括两个阶段，在状态估计和参数估计之间交替迭代，直到满足预定标准。具体而言，第一步，将模型参数视为已知，使用Rauch-Tung-Striebel（RTS）平滑器从可用测量中推断潜在状态；第二步，将平滑后的轨迹视为已知，通过反向传播估计神经网络参数。我们在部分状态观测下的线性、非线性和刚性动力学的基准系统上评估了该方法。在这些设置中，该方法从不完整测量中学习缺失的ODE组件，同时利用并保留可解释的机制结构，改善潜在状态重建和长期预测。
英文摘要：
Ordinary differential equations (ODEs) are widely used to model dynamical systems in physics, biology, neuroscience, and physiology, but in many applications some equations of the dynamics are unknown and only a subset of the state variables are measured. We propose a hybrid neural--physics framework in which the known components of the ODE are kept explicit and the missing components are represented by a neural network. The proposed method consists of two stages where we alternate between state and parameter estimation and iterate until a predetermined criterion is met. Specifically, in the first step, we treat the model parameters as being known and we infer the latent states from the available measurements using a Rauch--Tung--Striebel (RTS) smoother. In the second stage, we treat the smoothed trajectories as being known and use them to estimate the neural networks' parameters through backpropagation. We evaluate the method on benchmark systems spanning linear, nonlinear, and stiff dynamics under partial state observation. Across these settings, the proposed method learns missing ODE components from incomplete measurements while exploiting and retaining interpretable mechanistic structure and improving latent-state reconstruction and long-horizon prediction.
