Related papers: The Augmented Potential Method: Multiscale Modelin…

In this paper, we develop a numerical multiscale method to solve elliptic boundary value problems with heterogeneous diffusion coefficients and with singular source terms. When the diffusion coefficient is heterogeneous, this adds to the…

This dissertation explores block decomposable methods for large-scale optimization problems. It focuses on alternating direction method of multipliers (ADMM) schemes and block coordinate descent (BCD) methods. Specifically, it introduces a…

We consider a global variable consensus ADMM algorithm for solving large-scale PDE parameter estimation problems asynchronously and in parallel. To this end, we partition the data and distribute the resulting subproblems among the available…

Chemical segregation and structural transitions at interfaces are important nanoscale phenomena, making them natural targets for atomistic modeling, yet interatomic potentials must be fit to secondary physical properties. To isolate the…

Grain boundary (GB) energy is a fundamental property that affects the form of grain boundary and plays an important role to unveil the behavior of polycrystalline materials. With a better understanding of grain boundary energy distribution…

Modeling distributions of covariates, or density estimation, is a core challenge in unsupervised learning. However, the majority of work only considers the joint distribution, which has limited utility in practical situations. A more…

A very active area of materials research is to devise methods that use machine learning to automatically extract predictive models from existing materials data. While prior examples have demonstrated successful models for some applications,…

We show that the Gaussian Approximation Potential machine learning framework can describe complex magnetic potential energy surfaces, taking ferromagnetic iron as a paradigmatic challenging case. The training database includes total…

The success of first principles electronic structure calculation for predictive modeling in chemistry, solid state physics, and materials science is constrained by the limitations on simulated length and time scales due to computational…

We introduce a local machine-learning method for predicting the electron densities of periodic systems. The framework is based on a numerical, atom-centred auxiliary basis, which enables an accurate expansion of the all-electron density in…

Robust clustering from incomplete data is an important topic because, in many practical situations, real data sets are heavy-tailed, asymmetric, and/or have arbitrary patterns of missing observations. Flexible methods and algorithms for…

The use of machine learning interatomic potentials (MLIPs) in simulations of materials is a state-of-the-art approach, which allows achieving nearly \textit{ab initio} accuracy with orders of magnitude less computational cost.…

Molecular dynamics simulations are an invaluable tool in numerous scientific fields. However, the ubiquitous classical force fields cannot describe reactive systems, and quantum molecular dynamics are too computationally demanding to treat…

Recently, machine learning potentials (MLP) largely enhances the reliability of molecular dynamics, but its accuracy is limited by the underlying $\textit{ab initio}$ methods. A viable approach to overcome this limitation is to refine the…

We present a scheme to obtain an inexpensive and reliable estimate of the uncertainty associated with the predictions of a machine-learning model of atomic and molecular properties. The scheme is based on resampling, with multiple models…

Powder bed fusion is a widely used additive manufacturing (AM) process for producing complex, small-batch parts that are impractical to manufacture using conventional methods. However, its broader adoption is hindered by process-induced…

Machine learning methods have nowadays become easy-to-use tools for constructing high-dimensional interatomic potentials with ab initio accuracy. Although machine learned interatomic potentials are generally orders of magnitude faster than…

Many processes of scientific and technological interest are characterized by time scales that render their simulation impossible if one uses present day simulation capabilities. To overcome this challenge a variety of enhanced simulation…

A machine-learned interatomic potential for Ge-rich Ge$_x$Te alloys has been developed aiming at uncovering the kinetics of phase separation and crystallization in these materials. The results are of interest for the operation of embedded…

One of the most significant current discussions in the field of data mining is classifying imbalanced data. In recent years, several ways are proposed such as algorithm level (internal) approaches, data level (external) techniques, and…