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Physical Sciences and Mathematics Commons™

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Statistics and Probability

Missouri University of Science and Technology

Series

2019

Articles 1 - 10 of 10

Full-Text Articles in Physical Sciences and Mathematics

Efficient Smooth Non-Convex Stochastic Compositional Optimization Via Stochastic Recursive Gradient Descent, Wenqing Hu, Chris Junchi Li, Xiangru Lian, Ji Liu, Huizhuo Yuan Dec 2019

Efficient Smooth Non-Convex Stochastic Compositional Optimization Via Stochastic Recursive Gradient Descent, Wenqing Hu, Chris Junchi Li, Xiangru Lian, Ji Liu, Huizhuo Yuan

Mathematics and Statistics Faculty Research & Creative Works

Stochastic compositional optimization arises in many important machine learning applications. The objective function is the composition of two expectations of stochastic functions, and is more challenging to optimize than vanilla stochastic optimization problems. In this paper, we investigate the stochastic compositional optimization in the general smooth non-convex setting. We employ a recently developed idea of Stochastic Recursive Gradient Descent to design a novel algorithm named SARAH-Compositional, and prove a sharp Incremental First-order Oracle (IFO) complexity upper bound for stochastic compositional optimization: 𝒪((n + m)1/2ε-2) in the finite-sum case and 𝒪(ε-3) in the online case. …

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A Multi-Step Approach To Modeling The 24-Hour Daily Profiles Of Electricity Load Using Daily Splines, Abdelmonaem Jornaz, V. A. Samaranayake Nov 2019

A Multi-Step Approach To Modeling The 24-Hour Daily Profiles Of Electricity Load Using Daily Splines, Abdelmonaem Jornaz, V. A. Samaranayake

Mathematics and Statistics Faculty Research & Creative Works

Forecasting of real-time electricity load has been an important research topic over many years. Electricity load is driven by many factors, including economic conditions and weather. Furthermore, the demand for electricity varies with time, with different hours of the day and different days of the week having an effect on the load. This paper proposes a hybrid load-forecasting method that combines classical time series formulations with cubic splines to model electricity load. It is shown that this approach produces a model capable of making short-term forecasts with reasonable accuracy. In contrast to forecasting models that utilize a multitude of regressor …

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Three-Dimensional Rotation Of Paramagnetic And Ferromagnetic Prolate Spheroids In Simple Shear And Uniform Magnetic Field, Christopher A. Sobecki, Yanzhi Zhang, Cheng Wang Oct 2019

Three-Dimensional Rotation Of Paramagnetic And Ferromagnetic Prolate Spheroids In Simple Shear And Uniform Magnetic Field, Christopher A. Sobecki, Yanzhi Zhang, Cheng Wang

Mathematics and Statistics Faculty Research & Creative Works

We examine a time-dependent, three-dimensional rotation of magnetic ellipsoidal particles in a two-dimensional, simple shear flow and a uniform magnetic field. We consider that the particles have paramagnetic and ferromagnetic properties, and we compare their rotational dynamics due to the strengths and directions of the applied uniform magnetic field. We determine the critical magnetic field strength that can pin the particles' rotations. Above the critical field strength, the particles' stable steady angles were determined. In a weak magnetic regime (below the critical field strength), a paramagnetic particle's polar angle will oscillate toward the magnetic field plane while its azimuthal angle …

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An Optimal Edg Method For Distributed Control Of Convection Diffusion Pdes, X. Zhang, Y. Zhang, John R. Singler Oct 2019

An Optimal Edg Method For Distributed Control Of Convection Diffusion Pdes, X. Zhang, Y. Zhang, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

We propose an embedded discontinuous Galerkin (EDG) method to approximate the solution of a distributed control problem governed by convection diffusion PDEs, and obtain optimal a priori error estimates for the state, dual state, their uxes, and the control. Moreover, we prove the optimize-then-discretize (OD) and discrtize-then-optimize (DO) approaches coincide. Numerical results confirm our theoretical results.

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On Nonoscillatory Solutions Of Three Dimensional Time-Scale Systems, Elvan Akin, Taher Hassan, Ozkan Ozturk, Ismail U. Tiryaki Sep 2019

On Nonoscillatory Solutions Of Three Dimensional Time-Scale Systems, Elvan Akin, Taher Hassan, Ozkan Ozturk, Ismail U. Tiryaki

Mathematics and Statistics Faculty Research & Creative Works

In this article, we classify nonoscillatory solutions of a system of three-dimensional time scale systems. We use the method of considering the sign of components of such solutions. Examples are given to highlight some of our results. Moreover, the existence of such solutions is obtained by Knaster's fixed point theorem.

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An Hdg Method For Dirichlet Boundary Control Of Convection Dominated Diffusion Pdes, Gang Chen, John R. Singler, Yangwen Zhang Aug 2019

An Hdg Method For Dirichlet Boundary Control Of Convection Dominated Diffusion Pdes, Gang Chen, John R. Singler, Yangwen Zhang

Mathematics and Statistics Faculty Research & Creative Works

We first propose a hybridizable discontinuous Galerkin (HDG) method to approximate the solution of a convection dominated Dirichlet boundary control problem without constraints. Dirichlet boundary control problems and convection dominated problems are each very challenging numerically due to solutions with low regularity and sharp layers, respectively. Although there are some numerical analysis works in the literature on diffusion dominated convection diffusion Dirichlet boundary control problems, we are not aware of any existing numerical analysis works for convection dominated boundary control problems. Moreover, the existing numerical analysis techniques for convection dominated PDEs are not directly applicable for the Dirichlet boundary control …

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On The Instabilities And Transitions Of The Western Boundary Current, Daozhi Han, Marco Hernandez, Quan Wang Jul 2019

On The Instabilities And Transitions Of The Western Boundary Current, Daozhi Han, Marco Hernandez, Quan Wang

Mathematics and Statistics Faculty Research & Creative Works

We study the stability and dynamic transitions of the western boundary currents in a rectangular closed basin. By reducing the infinite dynamical system to a finite dimensional one via center manifold reduction, we derive a non-dimensional transition number that determines the types of dynamical transition. We show by careful numerical evaluation of the transition number that both continuous transitions (supercritical Hopf bifurcation) and catastrophic transitions (subcritical Hopf bifurcation) can happen at the critical Reynolds number, depending on the aspect ratio and stratification. The regions separating the continuous and catastrophic transitions are delineated on the parameter plane.

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Positivity-Preserving, Energy Stable Numerical Schemes For The Cahn-Hilliard Equation With Logarithmic Potential, Wenbin Chen, Cheng Wang, Xiaoming Wang, Steven M. Wise Jun 2019

Positivity-Preserving, Energy Stable Numerical Schemes For The Cahn-Hilliard Equation With Logarithmic Potential, Wenbin Chen, Cheng Wang, Xiaoming Wang, Steven M. Wise

Mathematics and Statistics Faculty Research & Creative Works

In this paper we present and analyze finite difference numerical schemes for the Cahn-Hilliard equation with a logarithmic Flory Huggins energy potential. Both first and second order accurate temporal algorithms are considered. in the first order scheme, we treat the nonlinear logarithmic terms and the surface diffusion term implicitly and update the linear expansive term and the mobility explicitly. We provide a theoretical justification that this numerical algorithm has a unique solution, such that the positivity is always preserved for the logarithmic arguments, i.e., the phase variable is always between −1 and 1, at a point-wise level. in particular, our …

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Extensions Of Schauder's And Darbo's Fixed Point Theorems, Zhaocai Hao, Martin Bohner, Junjun Wang Jan 2019

Extensions Of Schauder's And Darbo's Fixed Point Theorems, Zhaocai Hao, Martin Bohner, Junjun Wang

Mathematics and Statistics Faculty Research & Creative Works

In this paper, some new extensions of Schauder's and Darbo's fixed point theorems are given. As applications of the main results, the existence of global solutions for first-order nonlinear integro-differential equations of mixed type in a real Banach space is investigated.

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A Second Order Bdf Numerical Scheme With Variable Steps For The Cahn-Hilliard Equation, Wenbin Chen, Xiaoming Wang, Yue Yan, Zhuying Zhang Jan 2019

A Second Order Bdf Numerical Scheme With Variable Steps For The Cahn-Hilliard Equation, Wenbin Chen, Xiaoming Wang, Yue Yan, Zhuying Zhang

Mathematics and Statistics Faculty Research & Creative Works

We present and analyze a second order in time variable step BDF2 numerical scheme for the Cahn-Hilliard equation. the construction relies on a second order backward difference, convex-splitting technique and viscous regularizing at the discrete level. We show that the scheme is unconditionally stable and uniquely solvable. in addition, under mild restriction on the ratio of adjacent time-steps, an optimal second order in time convergence rate is established. the proof involves a novel generalized discrete Gronwall-type inequality. as far as we know, this is the first rigorous proof of second order convergence for a variable step BDF2 scheme, even in …

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