Solving Differential Equations using Physics-Informed Deep Equilibrium Models
<|reference_start|>Solving Differential Equations using Physics-Informed Deep Equilibrium Models: 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.<|reference_end|>
@article{pacheco2024solving,
    title={Solving Differential Equations using Physics-Informed Deep Equilibrium
  Models},
    author={Bruno Machado Pacheco and Eduardo Camponogara},
    journal={arXiv preprint arXiv:2406.03472},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.03472},
    primaryClass={cs.LG cs.SY eess.SY}
}