Projected Neural Differential Equations for Power Grid Modeling with Constraints

Alistair White, Anna Büttner, Maximilian Gelbrecht, Niki Kilbertus, Frank Hellmann, Niklas Boers

Keywords: neural differential equations, neural ordinary differential equations, constraints, manifolds, power grids

TL;DR: We introduce a new method for constraining neural differential equations and test it on power grid models.

Abstract:

Neural differential equations offer a powerful approach for data-driven simulation.
However, many applications in science and engineering possess known constraints that should be obeyed by the learned model.
We introduce projected neural differential equations (PNDEs), a new method for constraining neural differential equations based on projection of the learned vector field to the tangent space of the constraint manifold.
In tests on two challenging examples from power grid modeling, PNDEs outperform existing methods while requiring fewer hyperparameters.
Our approach demonstrates significant potential for enhancing the modeling of constrained dynamical systems, particularly in complex domains like power grid dynamics where accuracy and reliability are essential.

Submission Number: 27