TransNet: Transferable Neural Networks for Partial Differential Equations

Understand

Transfer learning for partial differential equations (PDEs) is to develop a pre-trained neural network that can be used to solve a wide class of PDEs.

• Existing transfer learning approaches require much information of the target PDEs such as its formulation and/or data of its solution for pre-training.
• In this work, we propose to construct transferable neural feature spaces from purely function approximation perspectives without using PDE information.
• The construction of the feature space involves re-parameterization of the hidden neurons and uses auxiliary functions to tune the resulting feature space.