A physics informed neural network architecture for moving boundary problems in science and engineering.

Area of Science:

• Computational Science
• Applied Mathematics
• Machine Learning

Background:

• Moving boundary problems are crucial in science and engineering but pose challenges due to unknown interfaces.
• Traditional numerical methods struggle with the dynamic coupling between moving interfaces and system variables.
• Deep Learning offers new approaches, with Physics-Informed Neural Networks (PINNs) showing promise for solving Partial Differential Equations (PDEs).

Purpose of the Study:

• To develop a novel and general Physics-Informed Neural Network (PINN) architecture specifically designed for moving boundary problems.
• To address the limitations of existing methods in handling problems where the spatial domain evolves over time.
• To provide a more feasible and effective computational tool for complex moving boundary dynamics.

Main Methods:

• A novel PINN architecture employing two separate neural networks is proposed.
• One network predicts the free boundary, while the other predicts the dependent system variables.
• This mesh-free approach converts the PDE problem into an optimization task based on the governing equations' residual.

Main Results:

• The proposed PINN architecture successfully solves various moving boundary problems.
• It demonstrates effectiveness in scenarios with time-evolving spatial domains.
• Solutions obtained via PINNs show robustness and potential for complex simulations.

Conclusions:

• The novel PINN architecture offers a significant advancement for tackling moving boundary problems.
• It provides a more accessible and feasible alternative to traditional methods for complex dynamics.
• This approach establishes PINNs as a robust simulation platform for scientific and engineering applications.