Physics-Informed Machine Learning for Two-Phase Moving-Interface and Stefan Problems
The Stefan problem is a classical free-boundary problem that models phase-change processes and poses computational challenges due to its moving interface and nonlinear temperature-phase coupling. In this work, we develop a physics-informed neural network framework for solving two-phase Stefan problems. The proposed method explicitly tracks the interface motion and enforces the discontinuity in the temperature gradient across the interface while maintaining global consistency of the temperature field. Our approach employs two neural networks: one representing the moving interface and the other for the temperature field. The interface network allows rapid categorization of thermal diffusivity in the spatial domain, which is a crucial step for selecting training points for the temperature network. The temperature network's input is augmented with a modified zero-level set function to accurately capture the jump in its normal derivative across the interface. Numerical experiments on two-phase dynamical Stefan problems demonstrate the superior accuracy and effectiveness of our proposed method compared with the ones obtained by other neural network methodology in literature. The results indicate that the proposed framework offers a robust and flexible alternative to traditional numerical methods for solving phase-change problems governed by moving boundaries. In addition, the proposed method can capture an unstable interface evolution associated with the Mullins-Sekerka instability.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
A Physics Informed Neural Network (PINN) Methodology for Coupled Moving Boundary PDEs
Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraint…
Multi-Task LearningPhysics-Informed Neural Networks for Enhanced Interface Preservation in Lattice Boltzmann Multiphase Simulations
This paper presents an improved approach for preserving sharp interfaces in multiphase Lattice Boltzmann Method (LBM) simulations using Physics-Informed Neural Networks (PINNs). Interface diffusion is a common challenge …
Kolmogorov-Arnold Networks for Free-Boundary Partial Differential Equations
We study free-boundary problems within a physics-informed framework using Kolmogorov-Arnold network (KAN) approximations. The proposed approach incorporates obstacle constraints, partial differential equation (PDE) inequ…
Physics-informed machine learning for moving load problems
This paper presents a new approach to simulate forward and inverse problems of moving loads using physics-informed machine learning (PIML). Physics-informed neural networks (PINNs) utilize the underlying physics of movin…
Physics-informed machine learningA Rapid Physics-Informed Machine Learning Framework Based on Extreme Learning Machine for Inverse Stefan Problems
The inverse Stefan problem, as a typical phase-change problem with moving boundaries, finds extensive applications in science and engineering. Recent years have seen the applications of physics-informed neural networks (…