Related papers: A Unified Multiscale Auxiliary PINN Framework for …

In crystals, macroscopic technological properties such as thermal conductivity originate from the microscopic drift and scattering of phonons, commonly described by the Boltzmann Transport Equation (BTE). Despite its widespread use, the…

We apply physics-informed neural networks (PINNs) to first-order two-scale periodic asymptotic homogenization of the property tensor in a generic elliptic equation. The problem of lack of differentiability of property tensors at the sharp…

The accurate solution of nonlinear hyperbolic partial differential equations (PDEs) remains challenging due to steep gradients, discontinuities, and multiscale structures that make conventional solvers computationally demanding.…

Deep neural operators can learn operators mapping between infinite-dimensional function spaces via deep neural networks and have become an emerging paradigm of scientific machine learning. However, training neural operators usually requires…

The Boltzmann transport equation (BTE) has proven indispensable in elucidating quasiballistic heat dynamics. Experimental observations of nondiffusive thermal transients, however, are interpreted almost exclusively through purely diffusive…

Accurately and efficiently solving nonlinear differential equations is crucial for modeling dynamic behavior across science and engineering. Physics-Informed Neural Networks (PINNs) have emerged as a powerful solution that embeds physical…

Heat propagation is governed by phonon interactions and mathematically described by partial differential equations (PDEs), which link thermal transport to the intrinsic properties of materials. Conventional experimental techniques infer…

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…

In this paper, we propose a refinement strategy to the well-known Physics-Informed Neural Networks (PINNs) for solving partial differential equations (PDEs) based on the concept of Optimal Transport (OT). Conventional black-box PINNs…

Physics-informed neural networks (PINNs) are promising to replace conventional partial differential equation (PDE) solvers by offering more accurate and flexible PDE solutions. However, they are hampered by the relatively slow convergence…

Seismic wave forward and inverse modeling are fundamental tools for subsurface imaging and geological hazard assessment. Conventional grid-based numerical methods, such as finite-difference and finite-element approaches, often require dense…

In this paper, by utilizing the theory of matched asymptotic expansions, an efficient and accurate neural network method, named as "MAE-TransNet", is developed for solving singular perturbation problems in general dimensions, whose…

The identification of material parameters occurring in constitutive models has a wide range of applications in practice. One of these applications is the monitoring and assessment of the actual condition of infrastructure buildings, as the…

There has been a growing interest in the use of Deep Neural Networks (DNNs) to solve Partial Differential Equations (PDEs). Despite the promise that such approaches hold, there are various aspects where they could be improved. Two such…

Physics-Informed Neural Networks (PINNs) have emerged as powerful tools for solving partial differential equations (PDEs). However, training PINNs from scratch is often computationally intensive and time-consuming. To address this problem,…

In this paper we develop a neural network for the numerical simulation of time-dependent linear transport equations with diffusive scaling and uncertainties. The goal of the network is to resolve the computational challenges of…

The Radiative Transfer Equations (RTEs) exhibit high dimensionality and multiscale characteristics, rendering conventional numerical methods computationally intensive. Existing deep learning methods perform well in low-dimensional or linear…

We develop a physics-informed neural networks (PINNs) framework for the inverse scattering problem in nuclear physics and apply it to the $P_{3/2}$ partial wave of neutron-alpha elastic scattering. The radial potential is represented by a…

With the rapid advancement of graphical processing units, Physics-Informed Neural Networks (PINNs) are emerging as a promising tool for solving partial differential equations (PDEs). However, PINNs are not well suited for solving PDEs with…

Simulating solute transport in heterogeneous porous media poses computational challenges due to the high-resolution meshing required for traditional solvers. To overcome these challenges, this study explores a mesh-free method based on deep…