Related papers: Towards a Machine-Learned Poisson Solver for Low-T…
Passive Gamma Emission Tomography (PGET) is an IAEA-approved technique for verifying spent nuclear fuel assemblies prior to geological disposal. Reconstructing the emission and attenuation maps from PGET measurements is a nonlinear…
Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial…
We introduce a three-dimensional (3D) fully tensor train (TT)-assembled isogeometric analysis (IGA) framework, TT-IGA, for solving partial differential equations (PDEs) on complex geometries. Our method reformulates IGA discrete operators…
We present a hybrid quantum-classical electrostatic Particle-in-Cell (PIC) method, where the electrostatic field Poisson solver is implemented on a quantum computer simulator using a hybrid classical-quantum Neural Network (HNN) using…
Multi-task learning (MTL) is an inductive transfer mechanism designed to leverage useful information from multiple tasks to improve generalization performance compared to single-task learning. It has been extensively explored in traditional…
This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian…
Kinetic plasma simulations solve the Vlasov-Poisson or Vlasov-Maxwell equations to evolve scalar-variable distribution functions in position-velocity phase space and vector-variable electromagnetic fields in physical space. The…
Accurate modeling of heat flux in inertial confinement fusion plasmas requires closures that remain predictive far from local equilibrium and across disparate spatial and temporal resolutions. We develop a resolution-independent…
Incorporation of machine learning (ML) techniques into atomic-scale modeling has proven to be an extremely effective strategy to improve the accuracy and reduce the computational cost of simulations. It also entails conceptual and practical…
Additive manufacturing has enabled the fabrication of advanced reactor geometries, permitting larger, more complex design spaces. Identifying promising configurations within such spaces presents a significant challenge for current…
Common time-explicit numerical methods for kinetic simulations of plasmas in the low-collisions limit fall into two classes of algorithms: momentum conserving and energy conserving. Each has certain drawbacks. The PIC algorithm does not…
In this paper we develop a geometric version of the Hamilton-Jacobi equation in the Poisson setting. Specifically, we "geometrize" what is usually called a complete solution of the Hamilton-Jacobi equation. We use some well-known results…
Solvent environments play a central role in determining molecular structure, energetics, reactivity, and interfacial phenomena. However, modeling solvation from first principles remains difficult due to the complex interplay of interactions…
We introduce a new approach to the anisotropic Calder\'on problem, based on a map called Poisson embedding that identifies the points of a Riemannian manifold with distributions on its boundary. We give a new uniqueness result for a large…
Laser plasma instabilities (LPIs) have significant influences on the laser energy deposition efficiency, hot electron generation, and uniformity of irradiation in inertial confined fusion (ICF). In contrast to theoretical analysis of linear…
When learning simulations for modeling physical phenomena in industrial designs, geometrical variabilities are of prime interest. While classical regression techniques prove effective for parameterized geometries, practical scenarios often…
We present a simple and efficient MATLAB implementation of the linear virtual element method for the three dimensional Poisson equation. The purpose of this software is primarily educational, to demonstrate how the key components of the…
Resolving numerically Vlasov-Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm…
Detailed analysis of efficiency and pollutant emission characteristics of practical turbulent combustion devices using complex combustion kinetics often depend on the interactions between the combustion chemistry involving both gasses…
In this paper we apply the newly born choice theory of the shape parameters contained in the smooth radial basis functions to solve Poisson equations. Some people complain that Luh's choice theory, based on harmonic analysis, is…