相关论文: Solving high-dimensional nonlinear filtering probl…

Nonnegative Tucker decomposition (NTD) is a powerful tool for the extraction of nonnegative parts-based and physically meaningful latent components from high-dimensional tensor data while preserving the natural multilinear structure of…

Nonlinear filtering with correlated noise leads to a Duncan-Mortensen-Zakai (DMZ) equation in the form of a stochastic partial differential equation (SPDE). Unlike the independent noise case, the presence of correlation prevents the…

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

High-dimensional partial differential equations (PDEs) are ubiquitous in economics, science and engineering. However, their numerical treatment poses formidable challenges since traditional grid-based methods tend to be frustrated by the…

Tensor train decomposition is one of the most powerful approaches for processing high-dimensional data. For low-rank tensor train decomposition of large tensors, the alternating least squares (ALS) algorithm is widely used by updating each…

In this paper, we propose a general framework for solving high-dimensional partial differential equations with tensor networks. Our approach uses Monte-Carlo simulations to update the solution and re-estimates the new solution from samples…

It is of great interest to solve the inverse problem of stationary radiative transport equation (RTE) in optical tomography. The standard way is to formulate the inverse problem into an optimization problem, but the bottleneck is that one…

Particle breakage due to collisional interactions plays a vital role in the development of several phenomena in science and engineering. The nonlinear collisional breakage equations (NCBEs) are a significant set of equations in this…

Low-rank tensor estimation offers a powerful approach to addressing high-dimensional data challenges and can substantially improve solutions to ill-posed inverse problems, such as image reconstruction under noisy or undersampled conditions.…

Nonlinear filter has long been an important problem in practical industrial applications. The Yau-Yau method is a highly versatile framework that transforms nonlinear filtering problems into initial-value problems governed by the Forward…

This paper considers the network slicing (NS) problem which attempts to map multiple customized virtual network requests to a common shared network infrastructure and allocate network resources to meet diverse service requirements. This…

We present a neural network-based method for solving linear and nonlinear partial differential equations, by combining the ideas of extreme learning machines (ELM), domain decomposition and local neural networks. The field solution on each…

One of the main issues in computing a tensor decomposition is how to choose the number of rank-one components, since there is no finite algorithms for determining the rank of a tensor. A commonly used approach for this purpose is to find a…

Most state of the art deep neural networks are overparameterized and exhibit a high computational cost. A straightforward approach to this problem is to replace convolutional kernels with its low-rank tensor approximations, whereas the…

Computing low-rank approximations of kernel matrices is an important problem with many applications in scientific computing and data science. We propose methods to efficiently approximate and store low-rank approximations to kernel matrices…

Maximizing the Kullback-Leibler divergence (KLD) is a fundamental problem in waveform design for active sensing and hypothesis testing, as it directly relates to the error exponent of detection probability. However, the associated…

Tensor ring (TR) decomposition has recently received increased attention due to its superior expressive performance for high-order tensors. However, the applicability of traditional TR decomposition algorithms to real-world applications is…

In the last two decades, increased need for high-fidelity simulations of the time evolution and propagation of forces in granular media has spurred renewed interest in discrete element method (DEM) modeling of frictional contact. Force…

We present an efficient and robust numerical algorithm for solving the two-dimensional linear elasticity problem that combines the Quantized Tensor Train format and a domain partitioning strategy. This approach makes it possible to solve…

In this study, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equations. We propose an iterative algorithm that exploits the…