HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks
This addresses a computational bottleneck for researchers and practitioners in physics-informed machine learning by providing an efficient method for parameterized differential equations, though it is incremental as it builds on existing hypernetwork and PINN approaches.
The paper tackles the problem of solving differential equations at multiple parameterizations without increasing computational cost by proposing HyperPINN, which uses hypernetworks to generate neural network solutions from given parameterizations, resulting in small-sized networks that learn a family of solutions over a parameter space.
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.