Related papers: The Pulsar Magnetosphere with Machine Learning: Me…
Understanding the magnetic field environment around Mars and its response to upstream solar wind conditions provide key insights into the processes driving atmospheric ion escape. To date, global models of Martian induced magnetosphere have…
A procedure that allows study of unstable stability of a boundary layer between plasma and a magnetic field has been developed. Layer equilibrium for one reason or another is not set but follows from strict solution of kinetic equation with…
We find two families of analytic solutions to the ideal magnetohydrodynamics (iMHD) equations, in a class of 4-dimensional (4D) curved spacetimes. The plasma current is null, and as a result, the stress-energy tensor of the plasma itself…
We propose a novel non-negative spherical relaxation for optimization problems over binary matrices with injectivity constraints, which in particular has applications in multi-matching and clustering. We relax respective binary matrix…
We present a unified numerical method to determine the shapes of multiple Hele-Shaw bubbles in steady motion, and in the absence of surface tension, in three planar domains: free space, the upper half-plane, and an infinite channel. Our…
In this paper, we propose a novel machine learning method based on an adaptive tensor neural network subspace for solving quasiperiodic elliptic problems. To this end, we first provide a theoretical analysis of the associated quasiperiodic…
The inversion of spectropolarimetric observations of the solar upper atmosphere is one of the most challenging goals in solar physics. If we account for all relevant ingredients of the spectral line formation process, such as the…
For the extrapolation of magnetic fields into the solar corona from measurements taken in the photosphere (or chromosphere) force-free magnetic fields are typically used. This does not take into account that the lower layers of the solar…
The magnetospheric plasma distribution in the vicinity of a pulsar at various inclination angles is investigated using a new relativistic, parallel 3D Particle-In-Cell (PIC) code DYMPHNA3D. DYMPHNA3D uses a superposition of the…
Nonlinear force-free solutions for the magnetic field in the solar corona constructed using photospheric vector magnetic field boundary data suffer from a basic problem: the observed boundary data are inconsistent with the nonlinear…
In this work we design and analyze a free energy satisfying finite difference method for solving Poisson-Nernst-Planck equations in a bounded domain. The algorithm is of second order in space, with numerical solutions satisfying all three…
We propose a mesh-free policy iteration framework based on physics-informed neural networks (PINNs) for solving entropy-regularized stochastic control problems. The method iteratively alternates between soft policy evaluation and…
Considering the nonlinear electromagnetic field coupled to Einstein gravity in the presence of cosmological constant, we obtain a new class of $d$-dimensional magnetic brane solutions. This class of solutions yields a spacetime with a…
Motivated by recent research on Physics-Informed Neural Networks (PINNs), we make the first attempt to introduce the PINNs for numerical simulation of the elliptic Partial Differential Equations (PDEs) on 3D manifolds. PINNs are one of the…
A self-consistent electrodynamics of a particle accelerator in a rotating neutron-star magnetosphere is investigated on the two-dimensional poloidal plane. Solving the Poisson equation for the electrostatic potential together with the…
Non-linear differential equations are a fundamental tool to describe different phenomena in nature. However, we still lack a well-established method to tackle stiff differential equations. Here we present a machine learning framework to…
Physics-Informed Neural Networks (PINNs) solve physical systems by incorporating governing partial differential equations directly into neural network training. In electromagnetism, where well-established methodologies such as FDTD and FEM…
Physics-informed neural networks (PINN) have been widely used in computational physics to solve partial differential equations (PDEs). In this study, we propose an energy-embedding-based physics-informed neural network method for solving…
Time-dependent partial differential equations are a significant class of equations that describe the evolution of various physical phenomena over time. One of the open problems in scientific computing is predicting the behaviour of the…
Relativistic plasmas around compact objects can sometimes be approximated as being force-free. In this limit, the plasma inertia is negligible and the overall dynamics is governed by global electric currents. We present a novel numerical…