Related papers: Improving ideal MHD equilibrium accuracy with phys…
We modify an existing magnetohydrodynamics algorithm to make it more compatible with a dimensionally-split (DS) framework. It is based on the standard reconstruct-solve-average strategy (using a Riemann solver), and relies on constrained…
A promising approach to improve climate-model simulations is to replace traditional subgrid parameterizations based on simplified physical models by machine learning algorithms that are data-driven. However, neural networks (NNs) often lead…
In this study, we introduce a novel approach for deriving the solution of the ideal force-free steady-state pulsar magnetosphere in three dimensions. Our method involves partitioning the magnetosphere into the regions of closed and open…
A hybrid spectral/finite-element code is developed to numerically solve the resistive finite-pressure magnetohydrodynamic equilibria without the necessity of postulating nested magnetic flux surfaces in the non-axisymmetric toroidal…
One key in real-life Nash equilibrium applications is to calibrate players' cost functions. To leverage the approximation ability of neural networks, we proposed a general framework for optimizing and learning Nash equilibrium using neural…
Obtaining system parameters and reconstructing the full flow state from limited velocity observations using conventional fluid dynamics solvers can be prohibitively expensive. Here we employ machine learning algorithms to overcome the…
Based on neural network and adaptive subspace approximation method, we propose a new machine learning method for solving partial differential equations. The neural network is adopted to build the basis of the finite dimensional subspace.…
We present an algorithm for simulating the equations of ideal magnetohydrodynamics and other systems of differential equations on an unstructured set of points represented by sample particles. Local, third-order, least-squares, polynomial…
We propose a machine learning algorithm for solving finite-horizon stochastic control problems based on a deep neural network representation of the optimal policy functions. The algorithm has three features: (1) It can solve…
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…
An accurate impact parameter determination in a heavy ion collision is crucial for almost all further analysis. The capabilities of an artificial neural network are investigated to that respect. A novel input generation for the network is…
This study investigates the potential accuracy boundaries of physics-informed neural networks, contrasting their approach with previous similar works and traditional numerical methods. We find that selecting improved optimization algorithms…
We explore the suitability of deep learning to capture the physics of subgrid-scale ideal magnetohydrodynamics turbulence of 2-D simulations of the magnetized Kelvin-Helmholtz instability. We produce simulations at different resolutions to…
In this work, we investigate an indirect approach for the numerical solution of optimal control problems via neural networks. A customized neural network is constructed, where optimal state, co-state and control trajectories are…
We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…
In this paper, we propose, analyze, and test an efficient algorithm for computing ensemble average of incompressible magnetohydrodynamics (MHD) flows, where instances/members correspond to varying kinematic viscosity, magnetic diffusivity,…
Neural network-based methods have demonstrated effectiveness in solving high-dimensional Mean-Field Games (MFG) equilibria, yet ensuring mathematically consistent density-coupled evolution remains a major challenge. This paper proposes the…
This paper provides a new avenue for exploiting deep neural networks to improve physics-based simulation. Specifically, we integrate the classic Lagrangian mechanics with a deep autoencoder to accelerate elastic simulation of deformable…
We propose a combination of machine learning and flux limiting for property-preserving subgrid scale modeling in the context of flux-limited finite volume methods for the one-dimensional shallow-water equations. The numerical fluxes of a…
In this paper, we propose a novel $hr$-adaptive finite element method, enhanced by neural networks, for parabolic equations. The main challenge of the conventional $h$-adaptive finite element method is interpolating the finite element…