Neural Port-Hamiltonian Differential Algebraic Equations for Compositional Learning of Electrical Networks

TL;DR

This paper introduces neural port-Hamiltonian differential algebraic equations (N-PHDAEs) for modeling constrained electrical systems, improving prediction accuracy and enabling compositional learning of complex networks.

Contribution

The paper develops a novel neural DAE framework with an automatic differentiation-based training algorithm, enhancing modeling of coupled dynamical systems with algebraic constraints.

Findings

N-PHDAE achieves an order of magnitude better accuracy than baseline models.

The approach effectively models nonlinear circuit dynamics.

It enables compositional learning for large-scale electrical networks.

Abstract

We develop compositional learning algorithms for coupled dynamical systems, with a particular focus on electrical networks. While deep learning has proven effective at modeling complex relationships from data, compositional couplings between system components typically introduce algebraic constraints on state variables, posing challenges to many existing data-driven approaches to modeling dynamical systems. Towards developing deep learning models for constrained dynamical systems, we introduce neural port-Hamiltonian differential algebraic equations (N-PHDAEs), which use neural networks to parameterize unknown terms in both the differential and algebraic components of a port-Hamiltonian DAE. To train these models, we propose an algorithm that uses automatic differentiation to perform index reduction, automatically transforming the neural DAE into an equivalent system of neural ordinary differential equations (N-ODEs), for which established model inference and backpropagation methods exist. Experiments simulating the dynamics of nonlinear circuits exemplify the benefits of our approach: the proposed N-PHDAE model achieves an order of magnitude improvement in prediction accuracy and constraint satisfaction when compared to a baseline N-ODE over long prediction time horizons. We also validate the compositional capabilities of our approach through experiments on a simulated DC microgrid: we train individual N-PHDAE models for separate grid components, before coupling them to accurately predict the behavior of larger-scale networks.