Search Results - "Communications in mathematics and statistics"

Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations by E, Weinan, Han, Jiequn, Jentzen, Arnulf

“…We study a new algorithm for solving parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) in high dimension,…”
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The Deep Ritz Method: A Deep Learning-Based Numerical Algorithm for Solving Variational Problems by E, Weinan, Yu, Bing

“…We propose a deep learning-based method, the Deep Ritz Method, for numerically solving variational problems, particularly the ones that arise from partial…”
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A Proposal on Machine Learning via Dynamical Systems by E, Weinan

“…We discuss the idea of using continuous dynamical systems to model general high-dimensional nonlinear functions used in machine learning. We also discuss the…”
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Estimations of Bounds on the Multiplicative Fractional Integral Inequalities Having Exponential Kernels by Peng, Yu, Fu, Hao, Du, Tingsong

“…To investigate the fractional Hermite–Hadamard-type inequalities, a class of the multiplicative fractional integrals having exponential kernels is introduced…”
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On Some Results in the Theory of Finite Partially Soluble Groups by Skiba, Alexander N.

“…This article provides an overview of some recent results and ideas related to the study of finite groups depending on the restrictions on some systems of their…”
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Designing Optimal Large Four-Level Experiments: A New Technique Without Recourse to Optimization Softwares by Elsawah, A. M.

“…Experimental design is an effective statistical tool that is extensively applied in modern industry, engineering, and science. It is proved that experimental…”
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BI-GreenNet: Learning Green’s Functions by Boundary Integral Network by Lin, Guochang, Chen, Fukai, Hu, Pipi, Chen, Xiang, Chen, Junqing, Wang, Jun, Shi, Zuoqiang

“…Green’s function plays a significant role in both theoretical analysis and numerical computing of partial differential equations (PDEs). However, in most…”
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Triply Factorised Groups and the Structure of Skew Left Braces by Ballester-Bolinches, A., Esteban-Romero, R.

“…The algebraic structure of skew left brace has proved to be useful as a source of set-theoretic solutions of the Yang–Baxter equation. We study in this paper…”
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Cauchy-Stieltjes Kernel Families and Free Multiplicative Convolution by Fakhfakh, Raouf, Hassairi, Abdelhamid

“…In this paper, we determine the effect of the free multiplicative convolution on the pseudo-variance function of a Cauchy-Stieltjes kernel family. We then use…”
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Strong Overall Error Analysis for the Training of Artificial Neural Networks Via Random Initializations by Jentzen, Arnulf, Riekert, Adrian

“…Although deep learning-based approximation algorithms have been applied very successfully to numerous problems, at the moment the reasons for their performance…”
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Scale-Free Percolation in Continuum Space by Deprez, Philippe, Wüthrich, Mario V.

“…The study of real-life network modeling has become very popular in recent years. An attractive model is the scale-free percolation model on the lattice Z d , d…”
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Finite Groups Isospectral to Simple Groups by Grechkoseeva, Maria A., Mazurov, Victor D., Shi, Wujie, Vasil’ev, Andrey V., Yang, Nanying

“…The spectrum of a finite group is the set of element orders of this group. The main goal of this paper is to survey results concerning recognition of finite…”
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Learning Invariance Preserving Moment Closure Model for Boltzmann–BGK Equation by Li, Zhengyi, Dong, Bin, Wang, Yanli

“…As one of the main governing equations in kinetic theory, the Boltzmann equation is widely utilized in aerospace, microscopic flow, etc. Its high-resolution…”
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An Identity for Expectations and Characteristic Function of Matrix Variate Skew-normal Distribution with Applications to Associated Stochastic Orderings by Pu, Tong, Balakrishnan, Narayanaswamy, Yin, Chuancun

“…We establish an identity for E f Y - E f X , when X and Y both have matrix variate skew-normal distributions and the function f satisfies some weak conditions…”
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Existence and Convergence of Solutions for Nonlinear Elliptic Systems on Graphs by Xu, Jinyan, Zhao, Liang

“…We consider a kind of nonlinear systems on a locally finite graph G = ( V , E ) . We prove via the mountain pass theorem that this kind of systems has a…”
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On a Discriminator for the Polynomial $$f(x)=x^3+x by Yang, Quan-Hui, Zhao, Lilu

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Diagnostic Measures for Functional Linear Model with Nonignorable Missing Responses by Zhu, Yujian, Zhao, Puying

“…Assessing the influence of individual observations of the functional linear models is important and challenging, especially when the observations are subject…”
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Fully-Decoupled and Second-Order Time-Accurate Scheme for the Cahn–Hilliard Ohta–Kawaski Phase-Field Model of Diblock Copolymer Melt Confined in Hele–Shaw Cell by Cao, Junying, Zhang, Jun, Yang, Xiaofeng

“…In this work, we consider numerical approximations of the phase-field model of diblock copolymer melt confined in Hele–Shaw cell, which is a very complicated…”
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Signed Zero-Divisor Graphs Over Commutative Rings by Lu, Lu, Feng, Lihua, Liu, Weijun

“…In this paper, we define signed zero-divisor graphs over commutative rings and investigate the interplay between the algebraic properties of the rings and the…”
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Portfolio Management with Option Compensation Scheme Under Rank-Dependent Expected Utility by Yuan, Lvning, Bi, Xiuchun, Zhang, Shuguang

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