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The nonclassical transport equation models particle transport processes in which the particle flux does not decrease as an exponential function of the particle's free-path. Recently, a spectral approach was developed to generate…

Scalar extrapolation and convergence acceleration methods are central tools in numerical analysis for improving the efficiency of iterative algorithms and the summation of slowly convergent series. These methods construct transformed…

Deep learning involves a difficult non-convex optimization problem, which is often solved by stochastic gradient (SG) methods. While SG is usually effective, it may not be robust in some situations. Recently, Newton methods have been…

Slowly convergent series and sequences as well as divergent series occur quite frequently in the mathematical treatment of scientific problems. In this report, a large number of mainly nonlinear sequence transformations for the acceleration…

We present a novel acceleration technique for improving the convergence of source iteration for discrete ordinates transport calculations. Our approach uses the idea of the dynamic mode decomposition (DMD) to estimate the slowly decaying…

Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…

While the Boltzmann transport equation can accurately model transport problems with highly forward-peaked scattering, obtaining its solution can become arbitrarily slow due to near-unity spectral radius associated with source iteration.…

Route alignment design in surveying and transportation engineering frequently involves fixed waypoint constraints, where a path must precisely traverse specific coordinates. While existing literature primarily relies on geometric…

In recent years, convolutional neural networks (CNNs) have shown great performance in various fields such as image classification, pattern recognition, and multi-media compression. Two of the feature properties, local connectivity and…

Optimization acceleration techniques such as momentum play a key role in state-of-the-art machine learning algorithms. Recently, generic vector sequence extrapolation techniques, such as regularized nonlinear acceleration (RNA) of Scieur et…

Proximal methods are known to identify the underlying substructure of nonsmooth optimization problems. Even more, in many interesting situations, the output of a proximity operator comes with its structure at no additional cost, and…

This paper presents an accurate S$_N$ solver for slab geometry. For constant cross-section regions, it gives accurate angular fluxes without need of fine meshes or approximation of solution forms.

A pervasive approach in scientific computing is to express the solution to a given problem as the limit of a sequence of vectors or other mathematical objects. In many situations these sequences are generated by slowly converging iterative…

Based on SGD, previous works have proposed many algorithms that have improved convergence speed and generalization in stochastic optimization, such as SGDm, AdaGrad, Adam, etc. However, their convergence analysis under non-convex conditions…

Many recent works have designed accelerators for Convolutional Neural Networks (CNNs). While digital accelerators have relied on near data processing, analog accelerators have further reduced data movement by performing in-situ computation.…

We develop a randomized Newton method capable of solving learning problems with huge dimensional feature spaces, which is a common setting in applications such as medical imaging, genomics and seismology. Our method leverages randomized…

In this paper, we propose a Barrett-Garcke-Nurnberg (BGN) method for evolving geometries under general flows and present the corresponding convergence analysis. Specifically, we examine the scenario where a closed curve evolves according to…

In this paper, we present an efficient fully spectral approximation scheme for exploring the one-dimensional steady-state neutron transport equation. Our methodology integrates the spectral-(Petrov-)Galerkin scheme in the spatial dimension…

This paper is concerned with the convergence of a two-step modified Newton method for solving the nonlinear system arising from the minimal nonnegative solution of nonsymmetric algebraic Riccati equations from neutron transport theory. We…

Dual descent methods are commonly used to solve network optimization problems because their implementation can be distributed through the network. However, their convergence rates are typically very slow. This paper introduces a family of…