Solving Differential Equations using Physics-Informed Deep Equilibrium Models
This work advances computational techniques for solving initial value problems, with implications for scientific computing and engineering applications, but it appears incremental as it builds on existing methods.
The paper tackled solving initial value problems of ordinary differential equations by introducing Physics-Informed Deep Equilibrium Models (PIDEQs), combining deep equilibrium models and physics-informed neural networks, and validated them on the Van der Pol oscillator, showing efficiency and effectiveness.
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.