RTS Smoother-Guided Learning of Physics-Based Neural Differential Models
This work addresses the problem of learning unknown dynamics from incomplete measurements, which is common in physics, biology, and neuroscience, by combining mechanistic models with neural networks.
The paper proposes a hybrid neural-physics framework for learning missing components of ODEs from partial state observations, using an RTS smoother to infer latent states and backpropagation to train neural networks. The method improves latent-state reconstruction and long-horizon prediction across linear, nonlinear, and stiff dynamics benchmarks.
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.