Gene

Statistics

Parametric statistics

Physics

Mathematical optimization

Engineering

Mathematical analysis

Repressor

Nonlinear system

Operator (biology)

Boundary value problem

Chemistry

Applied mathematics

Science and engineering

Mathematics

Computer science

Partial derivative

Biochemistry

Engineering ethics

Quantum mechanics

Transcription factor

Partial differential equation

Science Advances

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 markedly 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 previously unexplored paradigm for modeling and simulation of nonlinear and nonequilibrium processes in science and engineering.

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