相关论文: Physics-Informed Neural Solvers for Periodic Quant…
We present simulation results on the structure and dynamics of micromagnetic point singularities with atomistic resolution. This is achieved by embedding an atomistic computational region into a standard micromagnetic algorithm. Several…
A primer on the Floquet theory of periodically time-dependent quantum systems is provided, and it is shown how to apply this framework for computing the quasienergy band structure governing the dynamics of ultracold atoms in driven optical…
We investigate the use of Physics-Informed Neural Networks (PINNs) for solving the wave equation. Whilst PINNs have been successfully applied across many physical systems, the wave equation presents unique challenges due to the multi-scale,…
We consider a model of an electron in a crystal moving under the influence of an external electric field: Schr\"{o}dinger's equation with a potential which is the sum of a periodic function and a general smooth function. We identify two…
Chebyshev polynomials have shown significant promise as an efficient tool for both classical and quantum neural networks to solve linear and nonlinear differential equations. In this work, we adapt and generalize this framework in a quantum…
In this paper we develop a class of efficient Galerkin boundary element methods for the solution of two-dimensional exterior single-scattering problems. Our approach is based upon construction of Galerkin approximation spaces confined to…
The tight-binding model of quantum particles on a honeycomb lattice is investigated in the presence of homogeneous magnetic field. Provided the magnetic flux per unit hexagon is rational of the elementary flux, the one-particle Hamiltonian…
Graph neural networks (GNNs) naturally align with sparse operators and unstructured discretizations, making them a promising paradigm for physics-informed machine learning in computational mechanics. Motivated by discrete physics losses and…
We have developed a novel differential equation solver software called PND based on the physics-informed neural network for molecular dynamics simulators. Based on automatic differentiation technique provided by Pytorch, our software allows…
Graphene-based hyperbolic metamaterials have been predicted to transport evanescent fields with extraordinarily large vacuum wave-vectors. It is particularly at much higher wave vector values that the commonly employed descriptional models…
We present an open-source Physics Informed Neural Network environment for simulations of transient phenomena on two-dimensional rectangular domains, with the following features: (1) it is compatible with Google Colab which allows automatic…
Physics-informed neural networks provide a mesh-free framework for solving partial differential equation-governed problems in solid mechanics. However, most existing formulations in linear elasticity still learn the displacement field…
The recent surge of interest in physics-informed neural network (PINN) methods has led to a wave of studies that attest to their potential for solving partial differential equations (PDEs) and predicting the dynamics of physical systems.…
We are interested in numerically solving a transitional model derived from the Bloch model. The Bloch equation describes the time evolution of the density matrix of a quantum system forced by an electromagnetic wave. In a high frequency and…
The neural network method of solving differential equations is used to approximate the electric potential and corresponding electric field in the slit-well microfluidic device. The device's geometry is non-convex, making this a challenging…
We present a procedure for the systematic estimation of the dispersion properties of linear discrete systems with periodic time-varying coefficients. The approach relies on the analysis of a single unit cell, making use of Bloch theorem…
The field of machine learning has drawn increasing interest from various other fields due to the success of its methods at solving a plethora of different problems. An application of these has been to train artificial neural networks to…
Periodic driving serves as an effective method for controlling the properties of physical systems. Called "Floquet engineering," it is a broad field of theoretical and experimental activity. Whereas original Floquet theory was proposed to a…
Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…
The notions of Bloch wave, crystal momentum, and energy bands are commonly regarded as unique features of crystalline materials with commutative translation symmetries. Motivated by the recent realization of hyperbolic lattices in circuit…