DAE-PINN: a physics-informed neural network model for simulating differential algebraic equations with application to power networks

Deep learning-based surrogate modeling is becoming a promising approach for learning and simulating dynamical systems. However, deep-learning methods find it very challenging to learn stiff dynamics. In this paper, we develop DAE-PINN, the first effective physics-informed deep-learning framework for learning and simulating the solution trajectories of nonlinear differential-algebraic equations (DAE). DAEs are used to model complex engineering systems, e.g., power networks, and present a “form” of infinite stiffness, which makes learning their solution trajectories challenging. 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 the solution trajectories of a three-bus power network.