What do physics-informed DeepONets learn? Understanding and improving training for scientific computing applications
This work addresses training challenges in physics-informed DeepONets for scientific computing, offering incremental improvements in error reduction and model efficiency.
The paper investigates what physics-informed DeepONets learn by analyzing the universality of extracted basis functions and their potential for model reduction, and proposes a transfer learning approach to improve training across related PDEs, resulting in significant error reduction and more effective basis functions.
Physics-informed deep operator networks (DeepONets) have emerged as a promising approach toward numerically approximating the solution of partial differential equations (PDEs). In this work, we aim to develop further understanding of what is being learned by physics-informed DeepONets by assessing the universality of the extracted basis functions and demonstrating their potential toward model reduction with spectral methods. Results provide clarity about measuring the performance of a physics-informed DeepONet through the decays of singular values and expansion coefficients. In addition, we propose a transfer learning approach for improving training for physics-informed DeepONets between parameters of the same PDE as well as across different, but related, PDEs where these models struggle to train well. This approach results in significant error reduction and learned basis functions that are more effective in representing the solution of a PDE.