相关论文: A Bootstrap Algebraic Multilevel method for Markov…

We propose a novel training method based on nonlinear multilevel minimization techniques, commonly used for solving discretized large scale partial differential equations. Our multilevel training method constructs a multilevel hierarchy by…

Categorizing individual cells into one of many known cell type categories, also known as cell type annotation, is a critical step in the analysis of single-cell genomics data. The current process of annotation is time-intensive and…

Stemmed from the derivation of the optimal control to a stochastic linear-quadratic control problem with Markov jumps, we study one kind of backward stochastic differential equations (BSDEs) that the generator f is affected by a Markovian…

In this article, we study the application of Multi-Level Monte Carlo (MLMC) approaches to numerical random homogenization. Our objective is to compute the expectation of some functionals of the homogenized coefficients, or of the…

In this paper, we give a numerical analysis for the transmission eigenvalue problem by the finite element method. A type of multilevel correction method is proposed to solve the transmission eigenvalue problem. The multilevel correction…

Simulation of multiphase poromechanics involves solving a multi-physics problem in which multiphase flow and transport are tightly coupled with the porous medium deformation. To capture this dynamic interplay, fully implicit methods, also…

Stochastic collocation methods for approximating the solution of partial differential equations with random input data (e.g., coefficients and forcing terms) suffer from the curse of dimensionality whereby increases in the stochastic…

Nesterov's accelerated gradient method (NAG) is widely used in problems with machine learning background including deep learning, and is corresponding to a continuous-time differential equation. From this connection, the property of the…

Graph neural networks (GNNs) have struggled to outperform traditional optimization methods on combinatorial problems, limiting their practical impact. We address this gap by introducing a novel chaining procedure for the graph alignment…

We consider an algebraic multigrid (AMG) scheme for the direct solution of complex- valued square linear systems based on a recursive 2 x 2 block partitioning of the coefficient matrix and study the optimal choices of its components. In…

In many numerical schemes, the computational complexity scales non-linearly with the problem size. Solving a linear system of equations using direct methods or most iterative methods is a typical example. Algebraic multi-grid (AMG) methods…

This article discusses the uncertainty quantification (UQ) for time-independent linear and nonlinear partial differential equation (PDE)-based systems with random model parameters carried out using sampling-free intrusive stochastic…

Bayesian mixture models are widely applied for unsupervised learning and exploratory data analysis. Markov chain Monte Carlo based on Gibbs sampling and split-merge moves are widely used for inference in these models. However, both methods…

We propose a new type of multilevel method for solving eigenvalue problems based on Newton iteration. With the proposed iteration method, solving eigenvalue problem on the finest finite element space is replaced by solving a small scale…

In the stochastic gradient descent (SGD) for sequential simulations such as the neural stochastic differential equations, the Multilevel Monte Carlo (MLMC) method is known to offer better theoretical computational complexity compared to the…

Artificial Neural Networks were recently shown to be an efficient representation of highly-entangled many-body quantum states. In practical applications, neural-network states inherit numerical schemes used in Variational Monte Carlo, most…

Recently, a novel bootstrap method for numerical calculations in matrix models and quantum mechanical systems is proposed. We apply the method to certain quantum mechanical systems derived from some well-known local toric Calabi-Yau…

Discrete-state, continuous-time Markov models are widely used in the modeling of biochemical reaction networks. Their complexity often precludes analytic solution, and we rely on stochastic simulation algorithms to estimate system…

We propose a new family of multilevel methods for unconstrained minimization. The resulting strategies are multilevel extensions of high-order optimization methods based on q-order Taylor models (with q >= 1) that have been recently…

Accurately detecting symbols transmitted over multiple-input multiple-output (MIMO) wireless channels is crucial in realizing the benefits of MIMO techniques. However, optimal MIMO detection is associated with a complexity that grows…