Related papers: Improving ideal MHD equilibrium accuracy with phys…

Neural networks are universal approximators and are studied for their use in solving differential equations. However, a major criticism is the lack of error bounds for obtained solutions. This paper proposes a technique to rigorously…

Training an artificial neural network involves an optimization process over the landscape defined by the cost (loss) as a function of the network parameters. We explore these landscapes using optimisation tools developed for potential…

With the increasing use of nonlinear devices in both generation and consumption of power, it is essential that we develop accurate and quick control for active filters to suppress harmonics. Time delays between input and output are…

We present pseudospectral direct-numerical-simulation (DNS) studies of the three-dimensional magnetohydrodynamic (MHD) equations (3DRFMHD) with a stochastic force that has zero mean and a variance $\sim k^{-3}$, where $k$ is the wavenumber,…

We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…

We present three-dimensional solutions of the magnetohydrostatic equations in the co-rotating frame of reference outside a magnetized rigidly rotating cylinder. We make no symmetry assumption for the magnetic field, but to be able to make…

Neural networks (NN) have been recently applied together with evolutionary algorithms (EAs) to solve dynamic optimization problems. The applied NN estimates the position of the next optimum based on the previous time best solutions. After…

Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. The principle idea is to use a neural network as a global ansatz function to partial…

This work explores the search for heterogeneous approximate multiplier configurations for neural networks that produce high accuracy and low energy consumption. We discuss the validity of additive Gaussian noise added to accurate neural…

Aims. Linear magnetohydrostatic (MHS) models of solar magnetic fields balance plasma pressure gradients, gravity and Lorentz forces where the current density is composed of a linear force-free component and a cross-field component that…

In this work we propose an extension of physics informed supervised learning strategies to parametric partial differential equations. Indeed, even if the latter are indisputably useful in many applications, they can be computationally…

Physics-informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have…

Despite the considerable success of neural networks in security settings such as malware detection, such models have proved vulnerable to evasion attacks, in which attackers make slight changes to inputs (e.g., malware) to bypass detection.…

Recently, designing neural solvers for large-scale linear systems of equations has emerged as a promising approach in scientific and engineering computing. This paper first introduce the Richardson(m) neural solver by employing a meta…

We examine the effect of accuracy of high-order spectral element methods, with or without adaptive mesh refinement (AMR), in the context of a classical configuration of magnetic reconnection in two space dimensions, the so-called…

In this work, we present a study combining two approaches in the context of solving PDEs: the continuous finite element method (FEM) and more recent techniques based on neural networks. In recent years, physics-informed neural networks…

The neural network-based approach to solving partial differential equations has attracted considerable attention due to its simplicity and flexibility in representing the solution of the partial differential equation. In training a neural…

Network compression reduces the computational complexity and memory consumption of deep neural networks by reducing the number of parameters. In SVD-based network compression, the right rank needs to be decided for every layer of the…

In this paper we introduce a new method for exact decomposition of propagating, nonlinear magnetohydrodynamic (MHD) disturbances into their component eigenenergies associated with the familiar slow, Alfv\'en, and fast wave eigenmodes, and…

We present a new numerical tool for solving the special relativistic ideal MHD equations that is based on the combination of the following three key features: (i) a one-step ADER discontinuous Galerkin (DG) scheme that allows for an…