RTS Smoother-Guided Learning of Physics-Based Neural Differential Models

2026-07-16

AI Summary

This work addresses the challenge of accurately modeling and predicting complex dynamical systems under partial observability and incomplete knowledge of system dynamics. The authors propose a hybrid neural–physical framework that preserves the structure of known differential equations while employing neural networks to represent unknown dynamical components. A two-stage alternating optimization strategy is introduced: first, latent states are estimated using a Rauch–Tung–Striebel (RTS) smoother, and then neural network parameters are updated via backpropagation through the smoothed trajectories. By integrating physical priors with data-driven learning, the method maintains interpretability while effectively recovering missing dynamics from sparse observations. Empirical evaluations demonstrate substantial improvements in both latent state reconstruction accuracy and long-term prediction performance across multiple benchmark systems, including linear, nonlinear, and stiff dynamical models.

Abstract

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.

Problem

• ordinary differential equations
• partial state observation
• missing dynamics
• latent state reconstruction
• physics-based modeling

Innovation

• neural ODE
• RTS smoother
• hybrid physics-neural modeling
• latent state estimation
• partial observation