  This paper introduces Physics-Informed Deep Equilibrium Models (PIDEQs) for
solving initial value problems (IVPs) of ordinary differential equations
(ODEs). Leveraging recent advancements in deep equilibrium models (DEQs) and
physics-informed neural networks (PINNs), PIDEQs combine the implicit output
representation of DEQs with physics-informed training techniques. We validate
PIDEQs using the Van der Pol oscillator as a benchmark problem, demonstrating
their efficiency and effectiveness in solving IVPs. Our analysis includes key
hyperparameter considerations for optimizing PIDEQ performance. By bridging
deep learning and physics-based modeling, this work advances computational
techniques for solving IVPs, with implications for scientific computing and
engineering applications.
