Neural DAEs: Constrained neural networks

Abstract: This article investigates the effect of explicitly adding auxiliary algebraic trajectory information to neural networks for dynamical systems. We draw inspiration from the field of differential-algebraic equations and differential equations on manifolds and implement related methods in residual neural networks, despite some fundamental scenario differences. Constraint or auxiliary information effects are incorporated through stabilization as well as projection methods, and we show when to use which method based on experiments involving simulations of multi-body pendulums and molecular dynamics scenarios. Several of our methods are easy to implement in existing code and have limited impact on training performance while giving significant boosts in terms of inference.