Solving Differential Equations using Physics-Informed Deep Equilibrium Models

• URL: http://arxiv.org/abs/2406.03472v2
• Date: Fri, 28 Jun 2024 17:44:28 GMT
• Title: Solving Differential Equations using Physics-Informed Deep Equilibrium Models
• Authors: Bruno Machado Pacheco, Eduardo Camponogara,
• Abstract summary: This paper introduces Physics-Informed Deep Equilibrium Models (PIDEQs) for solving initial value problems (IVPs) of ordinary differential equations (ODEs) By bridging deep learning and physics-based modeling, this work advances computational techniques for solving IVPs, with implications for scientific computing and engineering applications.
• Score: 4.237218036051422
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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