One-Shot Transfer Learning of Physics-Informed Neural Networks
arXiv:2110.11286
Abstract
Solving differential equations efficiently and accurately sits at the heart of progress in many areas of scientific research, from classical dynamical systems to quantum mechanics. There is a surge of interest in using Physics-Informed Neural Networks (PINNs) to tackle such problems as they provide numerous benefits over traditional numerical approaches. Despite their potential benefits for solving differential equations, transfer learning has been under explored. In this study, we present a general framework for transfer learning PINNs that results in one-shot inference for linear systems of both ordinary and partial differential equations. This means that highly accurate solutions to many unknown differential equations can be obtained instantaneously without retraining an entire network. We demonstrate the efficacy of the proposed deep learning approach by solving several real-world problems, such as first- and second-order linear ordinary equations, the Poisson equation, and the time-dependent Schrodinger complex-value partial differential equation.
ICML AI4Science Workshop 2022
References in corpus (9)
- Hamiltonian Graph Networks with ODE Integrators
- Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domains
- The first 100 days: modeling the evolution of the COVID-19 pandemic
- NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation framework
- Towards Optimally Weighted Physics-Informed Neural Networks in Ocean Modelling
- Solving Differential Equations Using Neural Network Solution Bundles
- Machine learning structure preserving brackets for forecasting irreversible processes
- Unsupervised Reservoir Computing for Solving Ordinary Differential Equations
- Learning Contact Dynamics using Physically Structured Neural Networks