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A new Particle-in-Cell (PIC) method, that conserves energy exactly, is presented. The particle equations of motion and the Maxwell's equations are differenced implicitly in time by the midpoint rule and solved concurrently by a…
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…
The Energy Conserving semi-implicit method (ECsim), presented by Lapenta in 2017, is a Particle in Cell (PIC) algorithm for the simulation of plasmas. Energy conservation is achieved within a semi-implicit formulation that does not require…
Despite the rapid development of computational hardware, the treatment of large and high dimensional data sets is still a challenging problem. This paper provides a twofold contribution to the topic. First, we propose a Gaussian Mixture…
We describe an initial implementation of an electrostatic Particle-in-Cell (ES-PIC) module with adaptive Cartesian mesh in our Unified Flow Solver framework. Challenges of PIC method with cell-based adaptive mesh refinement (AMR) are…
Convolved Gaussian Process (CGP) is able to capture the correlations not only between inputs and outputs but also among the outputs. This allows a superior performance of using CGP than standard Gaussian Process (GP) in the modelling of…
Gaussian Processes (GPs) are highly expressive, probabilistic models. A major limitation is their computational complexity. Naively, exact GP inference requires $\mathcal{O}(N^3)$ computations with $N$ denoting the number of modeled points.…
Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…
The recently developed energy conserving semi-implicit method (ECsim) for PIC simulation is applied to multiple scale problems where the electron-scale physics needs to be only partially retained and the interest is on the macroscopic or…
We introduce an extension of the particle-in-cell (PIC) method that captures the Landau collisional effects in the Vlasov-Maxwell-Landau equations. The method arises from a regularisation of the variational formulation of the Landau…
Learning of low dimensional structure in multidimensional data is a canonical problem in machine learning. One common approach is to suppose that the observed data are close to a lower-dimensional smooth manifold. There are a rich variety…
The composite current source (CCS) model has been adopted as an advanced timing model that represents the current behavior of cells for improved accuracy and better capability than traditional non-linear delay models (NLDM) to model complex…
A persistent challenge in predictive molecular modeling of thermoset polymers is to capture the effects of chemical composition and degree of crosslinking (DC) on dynamical and mechanical properties with high computational efficiency. We…
A recent paper by Huang et al. [Computer Physics Communications 207, 123 (2016)] thoroughly analyzed the Finite Grid Instability(FGI) and spectral fidelity of standard Particle-In-Cell (PIC) methods. Numerical experiments were carried out…
With the significant advancement in quantum computation in the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used…
Unsupervised learning has been widely used in many real-world applications. One of the simplest and most important unsupervised learning models is the Gaussian mixture model (GMM). In this work, we study the multi-task learning problem on…
Efficient exploration of parameter spaces is crucial to extract physical information about the Epoch of Reionization from various observational probes. To this end, we propose a fast technique based on Gaussian Process Regression (GPR)…
High-fidelity modeling of plasma-based acceleration (PBA) requires the use of 3D fully nonlinear and kinetic descriptions based on the particle-in-cell (PIC) method. Three-dimensional PIC algorithms based on the quasi-static approximation…
The Expectation-Maximization (EM) algorithm is one of the most popular methods used to solve the problem of parametric distribution-based clustering in unsupervised learning. In this paper, we propose to analyze a generalized EM (GEM)…
We propose a new multi-scale molecular dynamics simulation method which can achieve high accuracy and high sampling efficiency simultaneously without aforehand knowledge of the coarse grained (CG) potential and test it for a biomolecular…