相关论文: Physics-Informed Neural Solvers for Periodic Quant…
Physics-informed neural networks (PINNs) have recently become a new popular method for solving forward and inverse problems governed by partial differential equations (PDEs). However, in the flow around airfoils, the fluid is greatly…
This study establishes a non-Bloch band theory for time-modulated discrete mechanical systems. We consider simple mass-spring chains whose stiffness is periodically modulated in time. Using the temporal Floquet theory, the system is…
The Schr\"{o}dinger equation with random potentials is a fundamental model for understanding the behaviour of particles in disordered systems. Disordered media are characterised by complex potentials that lead to the localisation of…
In this work, a novel Eig-PIELM framework is proposed that extends physics-informed extreme learning machine for an efficient and accurate solution of linear eigenvalue problems. The method reformulates the governing differential equations…
A state-of-the-art method that combines a quantum computational algorithm and machine learning, so-called quantum machine learning, can be a powerful approach for solving quantum many-body problems. However, the research scope in the field…
We propose a physics-informed neural networks (PINNs) framework to solve the infinite-horizon optimal control problem of nonlinear systems. In particular, since PINNs are generally able to solve a class of partial differential equations…
We propose the use of physics-informed neural networks for solving the shallow-water equations on the sphere in the meteorological context. Physics-informed neural networks are trained to satisfy the differential equations along with the…
The paper presents an efficient and robust data-driven deep learning (DL) computational framework developed for linear continuum elasticity problems. The methodology is based on the fundamentals of the Physics Informed Neural Networks…
A wide range of applications in science and engineering involve a PDE model in a domain with perforations, such as perforated metals or air filters. Solving such perforated domain problems suffers from computational challenges related to…
Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to…
A large number of magnetohydrodynamic (MHD) equilibrium calculations are often required for uncertainty quantification, optimization, and real-time diagnostic information, making MHD equilibrium codes vital to the field of plasma physics.…
The Fokker-Planck (FP) equation governing the evolution of the probability density function (PDF) is applicable to many disciplines but it requires specification of the coefficients for each case, which can be functions of space-time and…
To obtain fast solutions for governing physical equations in solid mechanics, we introduce a method that integrates the core ideas of the finite element method with physics-informed neural networks and concept of neural operators. This…
In this paper, we consider the numerical solution of the one-dimensional Schr\"odinger equation with a periodic lattice potential and a random external potential. This is an important model in solid state physics where the randomness is…
In this paper, we show a physics-informed neural network solver for the time-dependent surface PDEs. Unlike the traditional numerical solver, no extension of PDE and mesh on the surface is needed. We show a simplified prior estimate of the…
We introduce a physics-informed neural framework for modeling static and time-dependent galactic gravitational potentials. The method combines data-driven learning with embedded physical constraints to capture complex, small-scale features…
In this paper, we explore the evolution of plane curves and surfaces governed by the hyperbolic mean curvature flow. We propose a mesh-free approach based on the physics-informed neural networks (PINNs), which eliminates the need for…
Physics-informed neural networks allow models to be trained by physical laws described by general nonlinear partial differential equations. However, traditional architectures struggle to solve more challenging time-dependent problems due to…
Neural Operators (NOs) provide a powerful framework for computations involving physical laws that can be modelled by (integro-) partial differential equations (PDEs), directly learning maps between infinite-dimensional function spaces that…
Form-finding of unilateral membrane structures is commonly addressed by solving equilibrium equations with Finite Element Methods (FEMs). This paper investigates Physics-Informed Neural Networks (PINNs) as an alternative, where the…