Related papers: Towards a Machine-Learned Poisson Solver for Low-T…
Hamiltonian particle-based simulations of plasma dynamics are inherently computationally intensive, primarily due to the large number of particles required to obtain accurate solutions. This challenge becomes even more acute in many-query…
Detecting and analyzing the local environment is crucial for investigating the dynamical processes of crystal nucleation and shape colloidal particle self-assembly. Recent developments in machine learning provide a promising avenue for…
Geometry Problem Solving (GPS), which is a classic and challenging math problem, has attracted much attention in recent years. It requires a solver to comprehensively understand both text and diagram, master essential geometry knowledge,…
In computer chip manufacturing, the study of etch patterns on silicon wafers, or metrology, occurs on the nano-scale and is therefore subject to large variation from small, yet significant, perturbations in the manufacturing environment. An…
Despite the fundamental nature of the inhomogeneous Poisson process in the theory and application of stochastic processes, and its attractive generalizations (e.g. Cox process), few tractable nonparametric modeling approaches of intensity…
The Poisson equation has wide applications in many areas of science and engineering. Although there are some quantum algorithms that can efficiently solve the Poisson equation, they generally require a fault-tolerant quantum computer which…
Machine learning is applied to investigate the phase transition of two-dimensional complex plasmas. The Langevin dynamics simulation is employed to prepare particle suspensions in various thermodynamic states. Based on the resulted particle…
Vico et al. (2016) suggest a fast algorithm for computing volume potentials, beneficial to fields with problems requiring the solution of the free-space Poisson's equation, such as beam and plasma physics. Currently, the standard is the…
Recent advances in deep learning have inspired numerous works on data-driven solutions to partial differential equation (PDE) problems. These neural PDE solvers can often be much faster than their numerical counterparts; however, each…
We present VarP-GP, a new cost-efficient Bayesian emulator for expensive computational models with variable statistical precision. We focus on the interpretation of measurements of the quark-gluon plasma (QGP) generated in high-energy…
We discuss the scalable parallel solution of the Poisson equation within a Particle-In-Cell (PIC) code for the simulation of electron beams in particle accelerators of irregular shape. The problem is discretized by Finite Differences.…
A unified simulator that can model diverse physical phenomena without solver-specific redesign is a long-standing goal across simulation science. We present a learning-based particle simulator built on a single transformer architecture to…
With the rapid advancement of graphical processing units, Physics-Informed Neural Networks (PINNs) are emerging as a promising tool for solving partial differential equations (PDEs). However, PINNs are not well suited for solving PDEs with…
Solving a Poisson equation is generally reduced to solving a linear system with a coefficient matrix $A$ of entries $a_{ij}$, $i,j=1,2,...,n$, from the discretized Poisson equation. Although the variational quantum algorithms are promising…
Using detailed simulations of calorimeter showers as training data, we investigate the use of deep learning algorithms for the simulation and reconstruction of particles produced in high-energy physics collisions. We train neural networks…
"AI for science" is widely recognized as a future trend in the development of scientific research. Currently, although machine learning algorithms have played a crucial role in scientific research with numerous successful cases, relatively…
We present an analysis of different methods to calculate the classical electrostatic Hartree potential created by charge distributions. Our goal is to provide the reader with an estimation on the performance ---in terms of both numerical…
It is expected that progress toward true artificial intelligence will be achieved through the emergence of a system that integrates representation learning and complex reasoning (LeCun et al. 2015). In response to this prediction, research…
We consider the distributed training of large-scale neural networks that serve as PDE solvers producing full field outputs. We specifically consider neural solvers for the generalized 3D Poisson equation over megavoxel domains. A scalable…
Can neural networks learn to solve partial differential equations (PDEs)? We investigate this question for two (systems of) PDEs, namely, the Poisson equation and the steady Navier--Stokes equations. The contributions of this paper are…