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The entropy computation of Gaussian mixture distributions with a large number of components has a prohibitive computational complexity. In this paper, we propose a novel approach exploiting the sphere decoding concept to bound and…
We review our recently developed methods for large-scale electronic structure calculations, both in one-electron theory and many-electron theory. The method are based on the density matrix representation, together with the Wannier state…
An accurate description of nonadiabatic dynamics of molecular species on metallic surfaces poses a serious computational challenge associated with a multitude of closely-spaced electronic states. We propose a mixed quantum-classical scheme…
Casting neural networks in generative frameworks is a highly sought-after endeavor these days. Contemporary methods, such as Generative Adversarial Networks, capture some of the generative capabilities, but not all. In particular, they lack…
Distributed Gaussian process (DGP) is a popular approach to scale GP to big data which divides the training data into some subsets, performs local inference for each partition, and aggregates the results to acquire global prediction. To…
Prevalent semantic segmentation solutions are, in essence, a dense discriminative classifier of p(class|pixel feature). Though straightforward, this de facto paradigm neglects the underlying data distribution p(pixel feature|class), and…
An approach is proposed to calculate Generalized Parton Distributions (GPDs) in a Constituent Quark Model (CQM) scenario, considering the constituent quarks as complex systems. The GPDs are obtained from the wave functions of the non…
Topological order of a topological phase of matter in two spacial dimensions is encoded by a unitary modular (tensor) category (UMC). A group symmetry of the topological phase induces a group symmetry of its corresponding UMC. Gauging is a…
We consider the matrix composite materials (CM) of either random (statistically homogeneous or inhomogeneous), periodic, or deterministic (neither random nor periodic) structures. CMs exhibit linear or nonlinear behavior, coupled or…
An extension of time-dependent density functional theory (TDDFT), the generalized time-dependent generator coordinate method (TDGCM), is applied to a study of induced nuclear fission dynamics. In the generalized TDGCM, the correlated…
A major concern in modern power systems is that the popularity and fluctuating characteristics of renewable energy may cause more and more transmission congestion events. Traditional congestion management modeling involves AC or DC power…
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified…
We consider the problem of clustering data points in high dimensions, i.e. when the number of data points may be much smaller than the number of dimensions. Specifically, we consider a Gaussian mixture model (GMM) with non-spherical…
Deep clustering as an important branch of unsupervised representation learning focuses on embedding semantically similar samples into the identical feature space. This core demand inspires the exploration of contrastive learning and…
Generative machine learning models like the Restricted Boltzmann Machine (RBM) provide a practical approach for ansatz construction within the quantum computing framework. This work introduces a method that efficiently leverages RBM and…
Forecasting on sparse multivariate time series (MTS) aims to model the predictors of future values of time series given their incomplete past, which is important for many emerging applications. However, most existing methods process MTS's…
On a compact complex manifold $(M, J)$ endowed with a holomorphic Poisson tensor $\pi_J$ and a deRham class $\alpha\in H^2(M, \mathbb R)$, we study the space of generalized K\"ahler (GK) structures defined by a symplectic form $F\in \alpha$…
Modeling potential alloys requires the exploration of all possible configurations of atoms. Additionally, modeling the thermal properties of materials requires knowledge of the possible ways of displacing the atoms. One solution to finding…
The most difficult aspect of the realistic modeling of granular materials is how to capture the real shape of the particles. Here we present a method to simulate granular materials with complex-shaped particles. The particle shape is…
This paper introduces the Gaussian multi-Graphical Model, a model to construct sparse graph representations of matrix- and tensor-variate data. We generalize prior work in this area by simultaneously learning this representation across…