Related papers: Physics-Informed Machine Learning for Two-Phase Mo…
We study the solutions of the one-phase supercooled Stefan problem with kinetic undercooling, which describes the freezing of a supercooled liquid, in one spatial dimension. Assuming that the initial temperature lies between the equilibrium…
The transport of heat and particles in the relatively collisional edge regions of magnetically confined plasmas is a scientifically challenging and technologically important problem. Understanding and predicting this transport requires the…
This work proposes a Variational Physics-Informed Neural Network (VPINN) framework that integrates the Petrov-Galerkin formulation with deep neural networks (DNNs) for solving one-dimensional singularly perturbed boundary value problems…
Transition prediction is an important aspect of aerodynamic design because of its impact on skin friction and potential coupling with flow separation characteristics. Traditionally, the modeling of transition has relied on correlation-based…
Accurately predicting vapor pressure is vital for various industrial and environmental applications. However, obtaining accurate measurements for all compounds of interest is not possible due to the resource and labor intensity of…
We propose physics-informed holomorphic neural networks (PIHNNs) as a method to solve boundary value problems where the solution can be represented via holomorphic functions. Specifically, we consider the case of plane linear elasticity…
Outdoor thermal comfort is a critical determinant of urban livability, particularly in hot desert climates where extreme heat poses challenges to public health, energy consumption, and urban planning. Mean Radiant Temperature ($T_{mrt}$) is…
The training of neural networks is a complex, high-dimensional, non-convex and noisy optimization problem whose theoretical understanding is interesting both from an applicative perspective and for fundamental reasons. A core challenge is…
Physics-informed neural network (PINN) is a data-driven solver for partial and ordinary differential equations(ODEs/PDEs). It provides a unified framework to address both forward and inverse problems. However, the complexity of the…
In this article we develop a Physics Informed Neural Network (PINN) approach to simulate ice sheet dynamics governed by the Shallow Ice Approximation. This problem takes the form of a time-dependent parabolic obstacle problem. Prior work…
Given the facts of the extensiveness of multi-material diffusion problems and the inability of the standard PINN(Physics-Informed Neural Networks) method for such problems, in this paper we present a novel PINN method that can accurately…
We consider the problem of recovering the initial condition in the one-dimensional one-phase Stefan problem for the heat equation from the knowledge of the position of the melting point. We first recall some properties of the free boundary…
In this work, we present a methodology using Physics Informed Neural Networks (PINNs) to determine the required velocity of a coolant, given inlet and outlet temperatures for a given heat flux in a multilayered metal-oxide-semiconductor…
We present a parametric finite element approximation of two-phase flow. This free boundary problem is given by the Stokes equations in the two phases, which are coupled via jump conditions across the interface. Using a novel variational…
As an emerging technology in deep learning, physics-informed neural networks (PINNs) have been widely used to solve various partial differential equations (PDEs) in engineering. However, PDEs based on practical considerations contain…
This work investigates a class of moving boundary problems related to a nonlinear evolution equation featuring an exponential source term. We establish a connection to Stefan-type problems, for different boundary conditions at the fixed…
For multilayer structures, interfacial failure is one of the most important elements related to device reliability. For cohesive zone modelling, traction-separation relations represent the adhesive interactions across interfaces. However,…
In this article, we develop a cut finite element method for one-phase Stefan problems, with applications in laser manufacturing. The geometry of the workpiece is represented implicitly via a level set function. Material above the…
Phase-field simulations provide mechanistic descriptions of microstructure evolution, but repeated high-fidelity integration over long horizons and broad parameter spaces remains computationally expensive. We present PFNet, a…
We study a class of one-dimensional interacting particle systems with random boundaries as a microscopic model for Stefan's melting and freezing problem. We prove that under diffusive rescaling these particle systems exhibit a hydrodynamic…