Physics-informed machine learning with optimization-based guarantees: Applications to AC power flow
Jordan Jalving, Michael Eydenberg, Logan Blakely, Anya Castillo, Zachary Kilwein, J. Kyle Skolfield, Fani Boukouvala, Carl D. Laird
Abstract
This manuscript presents a complete framework for the development and verification of physics-informed neural networks with application to the alternating-current power flow (ACPF) equations. Physics-informed neural networks (PINN)s have received considerable interest within power systems communities for their ability to harness underlying physical equations to produce simple neural network architectures that achieve high accuracy using limited training data. The methodology developed in this work builds on existing methods and explores new important aspects around the implementation of PINNs including: (i) obtaining operationally relevant training data, (ii) efficiently training PINNs and using pruning techniques to reduce their complexity, and (iii) globally verifying the worst-case predictions given known physical constraints. The methodology is applied to the IEEE-14 and 118 bus systems where PINNs show substantially improved accuracy in a data-limited setting and attain better guarantees with respect to worst-case predictions.