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The central aim of this paper is to implement Deep Autoencoder and Neighborhood Components Analysis (NCA) dimensionality reduction methods in Matlab and to observe the application of these algorithms on nine unlike datasets from UCI machine…

We explore linear and non-linear dimensionality reduction techniques for statistical inference of parameters in cosmology. Given the importance of compressing the increasingly complex data vectors used in cosmology, we address questions…

Molecular dynamics (MD) simulations provide detailed insight into atomic-scale mechanisms but are inherently restricted to small spatio-temporal scales. Coarse-grained molecular dynamics (CGMD) techniques allow simulations of much larger…

Atomistic simulations with methods such as molecular dynamics are extremely powerful tools to understand nanoscale dynamical behavior. The resulting trajectories, by the virtue of being embedded in a high-dimensional configuration space,…

A long-standing challenge encountered in modeling plasma dynamics is achieving practical Vlasov equation simulation in multiple spatial dimensions over large length and time scales. While direct multi-dimension Vlasov simulation methods…

The rampdown phase of a tokamak pulse is difficult to simulate and often exacerbates multiple plasma instabilities. To reduce the risk of disrupting operations, we leverage advances in Scientific Machine Learning (SciML) to combine physics…

We numerically describe the physical mechanism underlying the terahertz photoconductive antenna (PCA) by the finite-difference time-domain method in three-dimension. The feature of our approach is that the multi-physical phenomena happening…

All-atom and coarse-grained molecular dynamics are two widely used computational tools to study the conformational states of proteins. Yet, these two simulation methods suffer from the fact that without access to supercomputing resources,…

We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…

Characterizing quantum dynamics is essential for quantifying arbitrary properties of a quantum process -- such as its ability to exhibit quantum-mechanical dynamics or generate entanglement. However, current methods require a number of…

Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…

Molecular dynamics (MD) simulations of successive collision cascades within the same simulation domain were performed using two different inter-atomic potentials (IAP) in tungsten, one EAM based and the other a `quantum accurate' machine…

Metastability is a common obstacle to performing long molecular dynamics simulations. Many numerical methods have been proposed to overcome it. One method is parallel replica dynamics, which relies on the rapid convergence of the underlying…

At the core of some of the most important problems in plasma physics -- from controlled nuclear fusion to the acceleration of cosmic rays -- is the challenge to describe nonlinear, multi-scale plasma dynamics. The development of reduced…

Handwritten digit images lie in a high-dimensional pixel space but exhibit strong geometric and statistical structure. This paper investigates the latent organization of handwritten digits in the MNIST dataset using three complementary…

Accelerating quantum dynamical simulations with quantum computing has received considerable attention but remains a significant challenge. In variational quantum algorithms for quantum dynamics, designing an expressive and shallow-depth…

Different unsupervised models for dimensionality reduction like PCA, LLE, Shannon's mapping, tSNE, UMAP, etc. work on different principles, hence, they are difficult to compare on the same ground. Although they are usually good for…

An efficient parallelization approach to simulate optical properties of ensembles of quantum emitters in realistic electromagnetic environments is considered. It relies on balancing computing load of utilized processors and is built into…

Many engineering processes can be accurately modelled using partial differential equations (PDEs), but high dimensionality and non-convexity of the resulting systems pose limitations on their efficient optimisation. In this work, a model…

Numerical simulation plays an important role in the study of structure formation of the universe. However, the mass resolution in current simulations is still poor. Due to technical difficulties, it is necessary to use both greatly reduced…