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Sanchita Malla1, Dietmar Oelz2, Sitikantha Roy3

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PubMed
Summary

This study introduces a novel Physics-Informed Neural Network (PINN) architecture to solve complex moving boundary problems. The new PINN approach effectively handles evolving spatial domains, offering a robust simulation platform for science and engineering.

Keywords:
Deep learningMoving boundary problemsNeural networks architecturePhysics-informed neural networks

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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.