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

Area of Science:

• Mathematics
• Computer Science
• Physics

Background:

• Partial differential equations (PDEs) are fundamental in science and engineering.
• Solving PDEs often involves computationally intensive methods, especially for multiple scenarios.
• Existing methods face challenges in modeling complex nonlinear and nonequilibrium processes.

Purpose of the Study:

• Introduce a novel deep learning framework, physics-informed DeepONets.
• Enable learning of solution operators for arbitrary PDEs.
• Overcome limitations of traditional PDE solvers.

Main Methods:

• Developed a deep learning framework integrating physical laws into neural networks.
• Trained DeepONets to learn the mapping from PDE parameters to solutions.
• Demonstrated capability without requiring paired input-output training data.

Main Results:

• Physics-informed DeepONets effectively learn PDE solution operators.
• Achieved prediction speeds up to three orders of magnitude faster than conventional solvers.
• Showcased applicability to various types of parametric PDEs.

Conclusions:

• Physics-informed DeepONets present a paradigm shift in PDE modeling and simulation.
• This framework accelerates the investigation of complex dynamic processes.
• Enables efficient exploration of nonlinear and nonequilibrium phenomena.