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The combinations of machine learning with ab initio methods have attracted much attention for their potential to resolve the accuracy-efficiency dilemma and facilitate calculations for large-scale systems. Recently, equivariant message…

The hierarchical Dirichlet process (HDP) has become an important Bayesian nonparametric model for grouped data, such as document collections. The HDP is used to construct a flexible mixed-membership model where the number of components is…

We propose a new random method to minimize deterministic continuous functions over subsets $\mathcal{S}$ of high-dimensional space $\mathbb{R}^K$ without assuming convexity. Our procedure alternates between a Global Search (GS) regime to…

This paper presents two novel ensemble domain decomposition methods for fast-solving the Stokes-Darcy coupled models with random hydraulic conductivity and body force. To address such random systems, we employ the Monte Carlo (MC) method to…

We propose an efficient way to sample from a class of structured multivariate Gaussian distributions which routinely arise as conditional posteriors of model parameters that are assigned a conditionally Gaussian prior. The proposed…

The first paper in this series introduced a new approach to strong convergence of random matrices that is based primarily on soft arguments. This method was applied to achieve a refined qualitative and quantitative understanding of strong…

Dimensionality reduction is crucial both for visualization and preprocessing high dimensional data for machine learning. We introduce a novel method based on a hierarchy built on 1-nearest neighbor graphs in the original space which is used…

We propose a slightly revised Miller-Hagberg (MH) algorithm that efficiently generates a random network from a given expected degree sequence. The revision was to replace the approximated edge probability between a pair of nodes with a…

Metaheuristic search methods have proven to be essential tools for tackling complex optimization challenges, but their full potential is often constrained by conventional algorithmic frameworks. In this paper, we introduce a novel approach…

This paper considers decentralized stochastic optimization over a network of $n$ nodes, where each node possesses a smooth non-convex local cost function and the goal of the networked nodes is to find an $\epsilon$-accurate first-order…

We study classes of Dynamic Programming (DP) algorithms which, due to their algebraic definitions, are closely related to coefficient extraction methods. DP algorithms can easily be modified to exploit sparseness in the DP table through…

Hybrid Monte-Carlo (HMC) sampling smoother is a fully non-Gaussian four-dimensional data assimilation algorithm that works by directly sampling the posterior distribution formulated in the Bayesian framework. The smoother in its original…

This work studies the problem of maximizing a higher degree real homogeneous multivariate polynomial over the unit sphere. This problem is equivalent to finding the leading eigenvalue of the associated symmetric tensor of higher order,…

The Euler Elastica (EE) model with surface curvature can generate artifact-free results compared with the traditional total variation regularization model in image processing. However, strong nonlinearity and singularity due to the…

Deep learning has gained significant attention in medical image segmentation. However, the limited availability of annotated training data presents a challenge to achieving accurate results. In efforts to overcome this challenge, data…

We consider the challenge of black-box optimization within hybrid discrete-continuous and variable-length spaces, a problem that arises in various applications, such as decision tree learning and symbolic regression. We propose DisCo-DSO…

Discovering a suitable neural network architecture for modeling complex dynamical systems poses a formidable challenge, often involving extensive trial and error and navigation through a high-dimensional hyper-parameter space. In this…

We present a novel computational approach to fast and memory-efficient deformable image registration. In the variational registration model, the computation of the objective function derivatives is the computationally most expensive…

The high-dimensional rank lasso (hdr lasso) model is an efficient approach to deal with high-dimensional data analysis. It was proposed as a tuning-free robust approach for the high-dimensional regression and was demonstrated to enjoy…

This paper proposes a novel meta-learning approach to optimize a robust portfolio ensemble. The method uses a deep generative model to generate diverse and high-quality sub-portfolios combined to form the ensemble portfolio. The generative…