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We introduce a unified, flexible, and easy-to-implement framework of sufficient dimension reduction that can accommodate both linear and nonlinear dimension reduction, and both the conditional distribution and the conditional mean as the…
Variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm designed for noisy intermediate-scale quantum (NISQ) computers. It is promising for quantum chemical calculations (QCC) because it can calculate the ground-state…
Metasurfaces have become a promising means for manipulating optical wavefronts in flat and high-performance optical devices. Conventional metasurface device design relies on trial-and-error methods to obtain target electromagnetic (EM)…
Recent research has shown growing interest in modeling hypergraphs, which capture polyadic interactions among entities beyond traditional dyadic relations. However, most existing methodologies for hypergraphs face significant limitations,…
The decentralized gradient descent (DGD) algorithm, and its sibling, diffusion, are workhorses in decentralized machine learning, distributed inference and estimation, and multi-agent coordination. We propose a novel, principled framework…
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…
Distance metric learning (DML) approaches learn a transformation to a representation space where distance is in correspondence with a predefined notion of similarity. While such models offer a number of compelling benefits, it has been…
In this paper, we present an improved framework of the spectral-based Discrete Dislocation Dynamics (DDD) approach introduced in [1,2], that establishes a direct connection with the continuum Field Dislocation Mechanics (FDM) approach. To…
Decision tree (DT) attracts persistent research attention due to its impressive empirical performance and interpretability in numerous applications. However, the growth of traditional yet widely-used univariate decision trees (UDTs) is…
Predicting materials properties from composition or structure is of great interest to the materials science community. Deep learning has recently garnered considerable interest in materials predictive tasks with low model errors when…
In this paper, we address the problem of dynamic network embedding, that is, representing the nodes of a dynamic network as evolving vectors within a low-dimensional space. While the field of static network embedding is wide and…
Vector retrieval systems exhibit significant performance variance across queries due to heterogeneous embedding quality. We propose a lightweight framework for predicting retrieval performance at the query level by combining quantization…
The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…
In [Phys. Rev. Lett. 128, 013001 (2022)] a novel ground state method was proposed. It has been suggested that this $i$-DMFT would be a method within one-particle reduced density matrix functional theory (DMFT), capable of describing…
Deep learning approaches such as convolutional neural nets have consistently outperformed previous methods on challenging tasks such as dense, semantic segmentation. However, the various proposed networks perform differently, with behaviour…
The combination of deep learning and ab initio materials calculations is emerging as a trending frontier of materials science research, with deep-learning density functional theory (DFT) electronic structure being particularly promising. In…
We consider the vector embedding problem. We are given a finite set of items, with the goal of assigning a representative vector to each one, possibly under some constraints (such as the collection of vectors being standardized, i.e.,…
This paper presents a deep relational metric learning (DRML) framework for image clustering and retrieval. Most existing deep metric learning methods learn an embedding space with a general objective of increasing interclass distances and…
We introduce the first learning-based dense matching algorithm, termed Equirectangular Projection-Oriented Dense Kernelized Feature Matching (EDM), specifically designed for omnidirectional images. Equirectangular projection (ERP) images,…
Dynamic texture (DT) exhibits statistical stationarity in the spatial domain and stochastic repetitiveness in the temporal dimension, indicating that different frames of DT possess a high similarity correlation that is critical prior…