Related papers: Towards a Machine-Learned Poisson Solver for Low-T…
Removing geometrical details from a complex domain is a classical operation in computer aided design. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. However, depending on the…
The resolution of the Poisson equation is usually one of the most computationally intensive steps for incompressible fluid solvers. Lately, Deep Learning, and especially Convolutional Neural Networks (CNN), has been introduced to solve this…
The Poisson equation has applications across many areas of physics and engineering, such as the dynamic process simulation of ocean current. Here we present a quantum Fast Poisson Solver, including the algorithm and the complete and modular…
We describe an implementation to solve Poisson's equation for an isolated system on a unigrid mesh using FFTs. The method solves the equation globally on mesh blocks distributed across multiple processes on a distributed-memory parallel…
Solving differential equations is one of the most compelling applications of quantum computing. Most existing quantum algorithms addressing general ordinary and partial differential equations are thought to be too expensive to execute…
In this paper, we present a machine learning-based data generator framework tailored to aid researchers who utilize simulations to examine various physical systems or processes. High computational costs and the resulting limited data often…
This work delves into solving the two dimensional Poisson problem through the Finite Element Method which is relevant in various physical scenarios including heat conduction, electrostatics, gravity potential, and fluid dynamics. However,…
Many methods solve Poisson equations by using grid techniques which discretize the problem in each dimension. Most of these algorithms are subject to the curse of dimensionality, so that they need exponential runtime. In the paper "Quantum…
Implicit solvent models, such as Poisson-Boltzmann models, play important roles in computational studies of biomolecules. A vital step in almost all implicit solvent models is to determine the solvent-solute interface, and the solvent…
We present a new multi-fluid, multi-temperature plasma solver with adaptive Cartesian mesh (ACM) based on a full-Newton (non-linear, implicit) scheme for collisional low-temperature plasma. The particle transport is described using the…
Partial differential equations (PDEs) are often computationally challenging to solve, and in many settings many related PDEs must be be solved either at every timestep or for a variety of candidate boundary conditions, parameters, or…
The Poisson-Boltzmann equation is a widely used model to study the electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a mesh on the molecular surface only, yielding accurate…
Research on smooth vector graphics is separated into two independent research threads: one on interpolation-based gradient meshes and the other on diffusion-based curve formulations. With this paper, we propose a mathematical formulation…
We present the development and benchmarking of Poisson solvers for graphics processing units (GPUs). Implemented in the Astaroth platform, the solvers feature high computational efficiency. We present novel combinations of discretizations…
The use of machine learning algorithms is an attractive way to produce very fast detector simulations for scattering reactions that can otherwise be computationally expensive. Here we develop a factorised approach where we deal with each…
The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far, either suffer from lack of accuracy and/or are limited to very small sizes of the…
A three-dimensional (3D) Poisson solver with longitudinal periodic and transverse open boundary conditions can have important applications in beam physics of particle accelerators. In this paper, we present a fast efficient method to solve…
Particle-In-Cell (PIC) methods are frequently used for kinetic, high-fidelity simulations of plasmas. Implicit formulations of PIC algorithms feature strong conservation properties, up to numerical round-off errors, and are not subject to…
We introduce Poisson-response tensor-on-tensor regression (PToTR), a novel regression framework designed to handle tensor responses composed element-wise of random Poisson-distributed counts. Tensors, or multi-dimensional arrays, composed…
Statistical learning methods show great promise in providing an accurate prediction of materials and molecular properties, while minimizing the need for computationally demanding electronic structure calculations. The accuracy and…