Related papers: Unsupervised identification of crystal defects fro…

We study the fairness of dimensionality reduction methods for recommendations. We focus on the fundamental method of principal component analysis (PCA), which identifies latent components and produces a low-rank approximation via the…

Dimension reduction is useful for exploratory data analysis. In many applications, it is of interest to discover variation that is enriched in a "foreground" dataset relative to a "background" dataset. Recently, contrastive principal…

Scientists use mathematical modelling to understand and predict the properties of complex physical systems. In highly parameterised models there often exist relationships between parameters over which model predictions are identical, or…

Machine Learning Interatomic Potentials (MLIPs) achieve near ab initio accuracy at a fraction of the cost of quantum-mechanical simulations, yet they remain prone to silent failures on out-of-distribution configurations, making principled…

Feature selection is an essential problem in computer vision, important for category learning and recognition. Along with the rapid development of a wide variety of visual features and classifiers, there is a growing need for efficient…

We present a new technique called contrastive principal component analysis (cPCA) that is designed to discover low-dimensional structure that is unique to a dataset, or enriched in one dataset relative to other data. The technique is a…

The ability to quickly and accurately compute properties from atomic simulations is critical for advancing a large number of applications in chemistry and materials science including drug discovery, energy storage, and semiconductor…

Quantum algorithms speeding up classical counterparts are proposed for the problems: 1. Recognition of eigenvalues with fixed precision. Given a quantum circuit generating unitary mapping $U$ and a complex number the problem is to determine…

Molecular simulation technologies have afforded researchers a unique look into the nanoscale interactions driving physical processes. However, a limitation for molecular dynamics (MD) simulations is that they must be performed on…

The design of next-generation alloys through the Integrated Computational Materials Engineering (ICME) approach relies on multi-scale computer simulations to provide thermodynamic properties when experiments are difficult to conduct.…

In many reacting flow systems, the thermo-chemical state-space is known or assumed to evolve close to a low-dimensional manifold (LDM). Various approaches are available to obtain those manifolds and subsequently express the original…

Monitoring plankton populations in situ is fundamental to preserve the aquatic ecosystem. Plankton microorganisms are in fact susceptible of minor environmental perturbations, that can reflect into consequent morphological and dynamical…

Nucleation plays a critical role in the birth of crystals and is associated with a vast array of phenomena such as protein crystallization and ice formation in clouds. Despite numerous experimental and theoretical studies, many aspects of…

Crystal structure prediction (CSP) has emerged as one of the most important approaches for discovering new materials. CSP algorithms based on evolutionary algorithms and particle swarm optimization have discovered a great number of new…

Machine-learning potentials (MLPs) for atomistic simulations are a promising alternative to conventional classical potentials. Current approaches rely on descriptors of the local atomic environment with dimensions that increase…

Crucial to gaining control over crystallisation in multicomponent materials or accurately modelling rheological behaviour of magma flows is to understand the mechanisms by which crystal nuclei form. The microscopic nature of such nuclei,…

The ionization potential (IP) is an important parameter providing essential insights into the reactivity of chemical systems. IPs are also crucial for designing, optimizing, and understanding the functionality of modern technological…

Crystal structure prediction (CSP) is a useful tool in pharmaceutical development for identifying and assessing risks associated with polymorphism, yet widespread adoption has been hindered by high computational costs and the need for both…

Both Superconducting and Ion-Trap are leading quantum architectures common in the current landscape of the quantum computing field, each with distinct characteristics and operational constraints. Understanding and measuring the underlying…

This is a detailed tutorial paper which explains the Principal Component Analysis (PCA), Supervised PCA (SPCA), kernel PCA, and kernel SPCA. We start with projection, PCA with eigen-decomposition, PCA with one and multiple projection…