Solving Differential Equations using Physics-Informed Deep Equilibrium Models
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914851126771712 |
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| author | Pacheco, Bruno Machado Camponogara, Eduardo |
| author_facet | Pacheco, Bruno Machado Camponogara, Eduardo |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_03472 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solving Differential Equations using Physics-Informed Deep Equilibrium Models Pacheco, Bruno Machado Camponogara, Eduardo Machine Learning Systems and Control 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. |
| title | Solving Differential Equations using Physics-Informed Deep Equilibrium Models |
| topic | Machine Learning Systems and Control |
| url | https://arxiv.org/abs/2406.03472 |