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Transfer learning for partial differential equations (PDEs) is to develop apre-trained neural network that can be used to solve a wide class of PDEs.Existing transfer learning approaches require much information of the targetPDEs such as its formulation and/or data of its solution for pre-training. Inthis work, we propose to construct transferable neural feature spaces frompurely function approximation perspectives without using PDE information. Theconstruction of the feature space involves re-parameterization of the hiddenneurons and uses auxiliary functions to tune the resulting feature space.Theoretical analysis shows the high quality of the produced feature space,i.e., uniformly distributed neurons. Extensive numerical experiments verify theoutstanding performance of our method, including significantly improvedtransferability, e.g., using the same feature space for various PDEs withdifferent domains and boundary conditions, and the superior accuracy, e.g.,several orders of magnitude smaller mean squared error than the state of theart methods.

TransNet: Transferable Neural Networks for Partial Differential Equations