Related papers: Dimensionality reduction methods for molecular sim…
Particle discretizations of partial differential equations are advantageous for high-dimensional kinetic models in phase space due to their better scalability than continuum approaches with respect to dimension. Complex processes…
Clustering algorithms remain valuable tools for grouping and summarizing the most important aspects of data. Example areas where this is the case include image segmentation, dimension reduction, signals analysis, model order reduction,…
Datasets in high-dimension do not typically form clusters in their original space; the issue is worse when the number of points in the dataset is small. We propose a low-computation method to find statistically significant clustering…
Clustering is a fundamental unsupervised learning approach. Many clustering algorithms -- such as $k$-means -- rely on the euclidean distance as a similarity measure, which is often not the most relevant metric for high dimensional data…
In this paper, we evaluate dimensionality reduction methods in terms of difficulty in estimating visual information on original images from dimensionally reduced ones. Recently, dimensionality reduction has been receiving attention as the…
Sintering, as a thermal process at elevated temperature below the melting point, is widely used to bond contacting particles into engineering products such as ceramics, metals, polymers, and cemented carbides. Modelling and simulation as…
Multi-component polymer systems are of interest in organic photovoltaic and drug delivery applications, among others where diverse morphologies influence performance. An improved understanding of morphology classification, driven by…
Markov state models (MSMs) have been successful in computing metastable states, slow relaxation timescales and associated structural changes, and stationary or kinetic experimental observables of complex molecules from large amounts of…
Subspace clustering refers to the problem of clustering high-dimensional data into a union of low-dimensional subspaces. Current subspace clustering approaches are usually based on a two-stage framework. In the first stage, an affinity…
Molecular Representation Learning (MRL) has emerged as a powerful tool for drug and materials discovery in a variety of tasks such as virtual screening and inverse design. While there has been a surge of interest in advancing model-centric…
The molecular simulations solve the equation of motion of molecular systems, making 3D shapes of molecules four-dimensional by adding the time coordinate. These methods have a great potential in drug discovery because they can realistically…
This paper addresses the problem of mapping high-dimensional data to a low-dimensional space, in the presence of other known features. This problem is ubiquitous in science and engineering as there are often controllable/measurable features…
Constructing reduced representations of high-dimensional systems is a fundamental problem in physical chemistry. Many unsupervised machine learning methods can automatically find such low-dimensional representations. However, an often…
Low-dimensional embeddings for data from disparate sources play critical roles in multi-modal machine learning, multimedia information retrieval, and bioinformatics. In this paper, we propose a supervised dimensionality reduction method…
In this paper, we consider the alignment between an upstream dimensionality reduction task of learning a low-dimensional representation of a set of high-dimensional data and a downstream optimization task of solving a stochastic program…
Clustering techniques are very attractive for extracting and identifying patterns in datasets. However, their application to very large spatial datasets presents numerous challenges such as high-dimensionality data, heterogeneity, and high…
Unsupervised machine learning lacks ground truth by definition. This poses a major difficulty when designing metrics to evaluate the performance of such algorithms. In sharp contrast with supervised learning, for which plenty of quality…
Microscopic processes on surfaces such as adsorption, desorption, diffusion and reaction of interacting particles can be simulated using kinetic Monte Carlo (kMC) algorithms. Even though kMC methods are accurate, they are computationally…
Computational models are quantitative representations of systems. By analyzing and comparing the outputs of such models, it is possible to gain a better understanding of the system itself. Though as the complexity of model outputs…
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…