Learning the solution operator of parametric partial differential equations with physics-informed DeepONets

Partial differential equations (PDEs) play a central role in the mathematical analysis and modeling of complex dynamic processes across all corners of science and engineering. Their solution often requires laborious analytical or computational tools, associated with a cost that is dramatically amplified when different scenarios need to be investigated, for example corresponding to different initial or boundary conditions, different inputs, etc. In this work we introduce physics-informed DeepONets; a deep learning framework for learning the solution operator of arbitrary PDEs, even in the absence of any paired input-output training data. We illustrate the effectiveness of the proposed framework in rapidly predicting the solution of various types of parametric PDEs up to three orders of magnitude faster compared to conventional PDE solvers, setting a new paradigm for modeling and simulation of non-linear and non-equilibrium processes in science and engineering.Jupyter notebooks to reproduce the numerical experiments