HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks

Filipe de Avila Belbute-Peres, Yi-fan Chen, Fei Sha

Keywords: pinn, physics-informed, physics informed neural networks, hypernetwork, physics, machine learning, deep learning, differential equation, pde, ode

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.

Publication Status: This work is unpublished.