DAE-PINN: A Physics-Informed Neural Network Model for Simulating Differential-Algebraic Equations with Application to Power Networks

TL;DR

This paper introduces DAE-PINN, a novel deep learning framework combining physics-informed neural networks and implicit Runge-Kutta schemes to effectively simulate nonlinear differential-algebraic equations, especially in power network dynamics.

Contribution

The paper presents the first effective deep-learning method for simulating stiff DAE systems, integrating implicit schemes with PINNs and enforcing DAEs as hard constraints.

Findings

Successfully models power network dynamics.

Accurately simulates long-term DAE trajectories.

Outperforms existing methods in handling stiffness.

Abstract

Deep learning-based surrogate modeling is becoming a promising approach for learning and simulating dynamical systems. Deep-learning methods, however, find very challenging learning stiff dynamics. In this paper, we develop DAE-PINN, the first effective deep-learning framework for learning and simulating the solution trajectories of nonlinear differential-algebraic equations (DAE), which present a form of infinite stiffness and describe, for example, the dynamics of power networks. Our DAE-PINN bases its effectiveness on the synergy between implicit Runge-Kutta time-stepping schemes (designed specifically for solving DAEs) and physics-informed neural networks (PINN) (deep neural networks that we train to satisfy the dynamics of the underlying problem). Furthermore, our framework (i) enforces the neural network to satisfy the DAEs as (approximate) hard constraints using a penalty-based method and (ii) enables simulating DAEs for long-time horizons. We showcase the effectiveness and accuracy of DAE-PINN by learning and simulating the solution trajectories of a three-bus power network.