Related papers: Physics-Informed Machine Learning for Two-Phase Mo…

We investigate the efficient learning of magnetic phases using artificial neural networks trained on synthetic data, combining computational simplicity with physics-informed strategies. Focusing on the diluted Ising model, which lacks an…

We consider a probabilistic formulation of a singular two-phase Stefan problem in one space dimension, which amounts to a coupled system of two McKean-Vlasov stochastic differential equations. In the financial context of systemic risk, this…

The computer simulation of quasistationary Stefan problem has been realized. Different representations of the Laplacian growth model are considered. The main attention has been paid for the interface dynamics represented by integro…

This paper presents computational analysis of the inverse Stefan type free boundary problem, where information on the boundary heat flux is missing and must be found along with the temperature and the free boundary. We pursue optimal…

So far the problem of interface behavior upon phase transition has not yet acquired a satisfactory mathematical formulation due to a variety of the physical phenomena involved. Analytical solutions exist only for elementary problems…

We present a novel physics-informed deep learning framework for solving steady-state incompressible flow on multiple sets of irregular geometries by incorporating two main elements: using a point-cloud based neural network to capture…

Simultaneously detecting hidden solid boundaries and reconstructing flow fields from sparse observations poses a significant inverse challenge in fluid mechanics. This study presents a physics-informed neural network (PINN) framework…

Modeling phase change problems numerically is vital for understanding many natural (e.g., ice formation, steam generation) and engineering processes (e.g., casting, welding, additive manufacturing). Almost all phase change materials (PCMs)…

We study the free boundary in the supercooled Stefan problem, a classical model for the solidification of water below its freezing temperature. In contrast with the melting problem, physical experiments and heuristics indicate that the…

We present accurate and mathematically consistent formulations of a diffuse-interface model for two-phase flow problems involving rapid evaporation. The model addresses challenges including discontinuities in the density field by several…

This paper presents a safe stabilization of the Stefan PDE model with a moving boundary governed by a high-order dynamics. We consider a parabolic PDE with a time-varying domain governed by a second-order response with respect to the…

We present PFNN, a penalty-free neural network method, to efficiently solve a class of second-order boundary-value problems on complex geometries. To reduce the smoothness requirement, the original problem is reformulated to a weak form so…

We present an algorithm for computing the nonlinear interface dynamics of the Mullins-Sekerka model for interfaces that are defined implicitly (e.g. by a level set function) using integral equations . The computation of the dynamics…

We consider a kinetic model of two species of particles interacting with a reservoir at fixed temperature, described by two coupled Vlasov-Fokker-Plank equations. We prove that in the diffusive limit the evolution is described by a…

This work presents a unified numerical framework for simulating incompressible flows within the coupled fluid-porous-medium system and involving heat and solute transport and phase-changing process. A complete set of governing equations is…

Estimating heat flux in the nuclear fusion device EAST is a critically important task. Traditional scientific computing methods typically model this process using the Finite Element Method (FEM). However, FEM relies on grid-based sampling…

Radiation heat transfer in a graded-index medium often suffers accuracy problems due to the gradual changes in the refractive index. The finite element method, meshfree, and other numerical methods often struggle to maintain accuracy when…

The application of deep learning methods to speed up the resolution of challenging power flow problems has recently shown very encouraging results. However, power system dynamics are not snap-shot, steady-state operations. These dynamics…

We present our deep learning framework to solve and accelerate the Time-Dependent partial differential equation's solution of one and two spatial dimensions. We demonstrate DiffusionNet solver by solving the 2D transient heat conduction…

The paper addresses a two-temperature model for simulating compressible two-phase flow taking into account diffusion processes related to the heat conduction and viscosity of the phases. This model is reduced from the two-phase…