TRASE-NODEs: Trajectory Sensitivity-aware Neural Ordinary Differential Equations for Efficient Dynamic Modeling

TL;DR

TRASE-NODEs introduce a trajectory sensitivity-aware neural ODE framework that improves data efficiency and prediction accuracy for dynamic systems by jointly modeling states and sensitivities.

Contribution

The paper presents TRASE-NODEs, a novel neural ODE approach that incorporates trajectory sensitivities for more efficient and accurate dynamic system modeling.

Findings

TRASE-NODEs outperform standard NODEs in prediction accuracy with limited data.

The framework effectively captures control set-point effects in dynamics.

Experimental results on damped oscillator and inverter-based resources validate the approach.

Abstract

Modeling dynamical systems is crucial across the science and engineering fields for accurate prediction, control, and decision-making. Recently, machine learning (ML) approaches, particularly neural ordinary differential equations (NODEs), have emerged as a powerful tool for data-driven modeling of continuous-time dynamics. Nevertheless, standard NODEs require a large number of data samples to remain consistent under varying control inputs, posing challenges to generate sufficient simulated data and ensure the safety of control design. To address this gap, we propose trajectory-sensitivity-aware (TRASE-)NODEs, which construct an augmented system for both state and sensitivity, enabling simultaneous learning of their dynamics. This formulation allows the adjoint method to update gradients in a memory-efficient manner and ensures that time-invariant control set-point effects are captured in the learned dynamics. We evaluate TRASE-NODEs using damped oscillator and inverter-based resources (IBRs). The results show that TRASE-NODEs generalize better from the limited training data, yielding lower prediction errors than standard NODEs for both examples. The proposed framework offers a data-efficient, control-oriented modeling approach suitable for dynamic systems that require accurate trajectory sensitivity prediction.