Related papers: Physics-Informed Neural Networks for Discovering L…

Traditional numerical methods often struggle with the complexity and scale of modeling pollutant transport across vast and dynamic oceanic domains. This paper introduces a Physics-Informed Neural Network (PINN) framework to simulate the…

The self-consistent theory of Anderson localization of quantum particles or classical waves in disordered media is reviewed. After presenting the basic concepts of the theory of Anderson localization in the case of electrons in disordered…

Physics-informed neural networks (PINNs) are an emerging technique to solve partial differential equations (PDEs). In this work, we propose a simple but effective PINN approach for the phase-field model of ferroelectric microstructure…

A physics-informed neural network (PINN) uses physics-augmented loss functions, e.g., incorporating the residual term from governing partial differential equations (PDEs), to ensure its output is consistent with fundamental physics laws.…

Physics-Informed Neural Networks (PINNs) have emerged as a promising framework for solving forward and inverse problems governed by differential equations. However, their reliability when used in ill-posed inverse problems remains poorly…

This study presents a novel physics-informed neural network (PINN) framework for modeling poroelasticity in heterogeneous media with material interfaces. The approach introduces a composite neural network (CoNN) where separate neural…

Physics-informed neural networks (PINNs) are revolutionizing science and engineering practice by bringing together the power of deep learning to bear on scientific computation. In forward modeling problems, PINNs are meshless partial…

The prediction non-equilibrium transport phenomena in disordered media is a difficult problem for conventional numerical methods. An example of a challenging problem is the prediction of gas flow fields through porous media in the rarefied…

Simulating discontinuities is a long standing problem especially for shock waves with strong nonlinear feather. Despite being a promising method, the recently developed physics-informed neural network (PINN) is still weak for calculating…

Anderson localisation is an important phenomenon arising in many areas of physics, and here we explore it in the context of quantum information devices. Finite dimensional spin chains have been demonstrated to be important devices for…

Physics-informed neural networks (PINNs) offer a novel AI-driven framework for integrating physical laws directly into neural network models, facilitating the solution of complex multiphysics problems in materials engineering. This study…

We demonstrate the utility of physics-informed neural networks (PINNs) as solvers for the non-relativistic, time-dependent Schr\"odinger equation. We study the performance and generalisability of PINN solvers on the time evolution of a…

Mode conversion in non-homogeneous elastic media makes it challenging to interpret physical properties accurately. Decomposing these modes correctly is crucial across various scientific areas. Recent machine learning approaches have been…

We present the first rigorous result on Anderson localization for interacting systems of quantum particles subject to a deterministic (e.g., almost periodic) disordered external potential. For a particular class of deterministic, fermionic,…

Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical…

Physics-informed neural networks (PINNs) have emerged as a new learning paradigm for solving partial differential equations (PDEs) by enforcing the constraints of physical equations, boundary conditions (BCs), and initial conditions (ICs)…

Physics informed neural network (PINN) based solution methods for differential equations have recently shown success in a variety of scientific computing applications. Several authors have reported difficulties, however, when using PINNs to…

When investigating epidemic dynamics through differential models, the parameters needed to understand the phenomenon and to simulate forecast scenarios require a delicate calibration phase, often made even more challenging by the scarcity…

In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…

We propose Gradient Informed Neural Networks (GradINNs), a methodology inspired by Physics Informed Neural Networks (PINNs) that can be used to efficiently approximate a wide range of physical systems for which the underlying governing…