HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks

• URL: http://arxiv.org/abs/2111.01008v1
• Date: Thu, 28 Oct 2021 17:50:09 GMT
• Title: HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks
• Authors: Filipe de Avila Belbute-Peres, Yi-fan Chen, Fei Sha
• Abstract summary: We propose the HyperPINN, which uses hypernetworks to learn to generate neural networks that can solve a differential equation from a given parameterization. We demonstrate with experiments on both a PDE and an ODE that this type of model can lead to neural network solutions to differential equations that maintain a small size.
• Score: 32.095262903584725
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Many types of physics-informed neural network models have been proposed in recent years as approaches for learning solutions to differential equations. When a particular task requires solving a differential equation at multiple parameterizations, this requires either re-training the model, or expanding its representation capacity to include the parameterization -- both solution that increase its computational cost. We propose the HyperPINN, which uses hypernetworks to learn to generate neural networks that can solve a differential equation from a given parameterization. We demonstrate with experiments on both a PDE and an ODE that this type of model can lead to neural network solutions to differential equations that maintain a small size, even when learning a family of solutions over a parameter space.

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