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The integration of Deep Learning (DL) into experimental nuclear and particle physics has driven significant progress in simulation and reconstruction workflows. However, traditional simulation frameworks such as Geant4 remain…

Local-gradient-based optimization approaches lack nonlocal exploration ability required for escaping from local minima in non-convex landscapes. A directional Gaussian smoothing (DGS) approach was recently proposed by the authors (Zhang et…

We consider stochastic strongly convex optimization with a complex inequality constraint. This complex inequality constraint may lead to computationally expensive projections in algorithmic iterations of the stochastic gradient…

Embedding parameterized optimization problems as layers into machine learning architectures serves as a powerful inductive bias. Training such architectures with stochastic gradient descent requires care, as degenerate derivatives of the…

The time-dependent radiation transport equation is discretized using the meshless-local Petrov-Galerkin method with reproducing kernels. The integration is performed using a Voronoi tessellation, which creates a partition of unity that only…

Logarithms of determinants of large positive definite matrices appear ubiquitously in machine learning applications including Gaussian graphical and Gaussian process models, partition functions of discrete graphical models, minimum-volume…

Accurate thermal analysis of composites and porous media requires detailed characterization of local thermal properties in small scale. For some important applications such as lithium-ion batteries, changes in the properties during the…

In this project, we propose a Variational Inference algorithm to approximate posterior distributions. Building on prior methods, we develop the Gradient-Steered Stein Variational Gradient Descent (G-SVGD) approach. This method introduces a…

We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an $\ell_0$-norm constraint. Through decomposing the feasible set of the given sparsity…

We consider the adaptive-rank integration of {2D and 3D} time-dependent advection-diffusion partial differential equations (PDEs) with variable coefficients. We employ a standard finite-difference method for spatial discretization coupled…

In this paper, we propose several novel deep learning methods for object saliency detection based on the powerful convolutional neural networks. In our approach, we use a gradient descent method to iteratively modify an input image based on…

In this paper we combine concepts from Riemannian Optimization and the theory of Sobolev gradients to derive a new conjugate gradient method for direct minimization of the Gross-Pitaevskii energy functional with rotation. The conservation…

A framework for Chebyshev spectral collocation methods for the numerical solution of functional and delay differential equations (FDEs and DDEs) is described. The framework combines interpolation via the barycentric resampling matrix with a…

In this paper, we introduce a novel estimator for vision-aided inertial navigation systems (VINS), the Preconditioned Cholesky-based Square Root Information Filter (PC-SRIF). When solving linear systems, employing Cholesky decomposition…

This work considers the problem of computing the canonical polyadic decomposition (CPD) of large tensors. Prior works mostly leverage data sparsity to handle this problem, which is not suitable for handling dense tensors that often arise in…

We present variants of the Conjugate Gradient (CG), Conjugate Residual (CR), and Generalized Minimal Residual (GMRES) methods which are both pipelined and flexible. These allow computation of inner products and norms to be overlapped with…

This paper proposes and develops new linesearch methods with inexact gradient information for finding stationary points of nonconvex continuously differentiable functions on finite-dimensional spaces. Some abstract convergence results for a…

This paper proposes a novel proximal-gradient algorithm for a decentralized optimization problem with a composite objective containing smooth and non-smooth terms. Specifically, the smooth and nonsmooth terms are dealt with by gradient and…

The idea of using fragment embedding to circumvent the high computational scaling of accurate electronic structure methods while retaining high accuracy has been a long-standing goal for quantum chemists. Traditional fragment embedding…

Zeroth-Order (ZO) optimization is pivotal for scenarios where backpropagation is unavailable, such as memory-constrained on-device learning and black-box optimization. However, existing methods face a stark trade-off: they are either…