相关论文: Multirate Exponential Rosenbrock Methods

This paper is focused on performing a new method for solving linear and nonlinear higher-order boundary value problems (HBVPs). This direct numerical method based on spectral method. The trial function of this method is the Monic Chebyshev…

In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for…

Highly concentrated functions play an important role in many research fields including control system analysis and physics, and they turned out to be the key idea behind inverse Laplace transform methods as well. This paper uses the…

We review the basic outline of the highly successful diffusion Monte Carlo technique commonly used in contexts ranging from electronic structure calculations to rare event simulation and data assimilation, and propose a new class of…

This paper studies empirical risk minimization (ERM) problems for large-scale datasets and incorporates the idea of adaptive sample size methods to improve the guaranteed convergence bounds for first-order stochastic and deterministic…

We propose a new method for low-rank approximation of Moore-Penrose pseudoinverses (MPPs) of large-scale matrices using tensor networks. The computed pseudoinverses can be useful for solving or preconditioning of large-scale overdetermined…

Accelerated first order methods, also called fast gradient methods, are popular optimization methods in the field of convex optimization. However, they are prone to suffer from oscillatory behaviour that slows their convergence when medium…

The direct deep learning simulation for multi-scale problems remains a challenging issue. In this work, a novel higher-order multi-scale deep Ritz method (HOMS-DRM) is developed for thermal transfer equation of authentic composite materials…

Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…

In this paper, we design high order accurate and stable finite difference schemes for the initial-boundary value problem, associated with the magnetic induction equation with resistivity. We use Summation-By-Parts (SBP) finite difference…

We introduce an efficient computational framework for solving a class of multi-marginal martingale optimal transport problems, which includes many robust pricing problems of large financial interest. Such problems are typically…

Exact methods for exponentiation of matrices of dimension $N$ can be computationally expensive in terms of execution time ($N^{3}$) and memory requirements ($N^{2}$) not to mention numerical precision issues. A type of matrix often…

The fundamental purpose of the present work is to constitute an enhanced Euler method with adaptive inverse-quadratic and inverse-multi-quadratic radial basis function (RBF) interpolation technique to solve initial value problems. These…

We construct an efficient class of increasingly high-order (up to 17th-order) essentially non-oscillatory schemes with multi-resolution (ENO-MR) for solving hyperbolic conservation laws. The candidate stencils for constructing ENO-MR…

Projected gradient descent and its Riemannian variant belong to a typical class of methods for low-rank matrix estimation. This paper proposes a new Nesterov's Accelerated Riemannian Gradient algorithm by efficient orthographic retraction…

In this paper, we derive a randomized version of the Mirror-Prox method for solving some structured matrix saddle-point problems, such as the maximal eigenvalue minimization problem. Deterministic first-order schemes, such as Nesterov's…

Invariant risk minimization (IRM) aims to enable out-of-distribution (OOD) generalization in deep learning by learning invariant representations. As IRM poses an inherently challenging bi-level optimization problem, most existing approaches…

In this paper, we propose a class of super-schemes for efficiently solving nonlinear unconstrained optimization problems. The proposed approach introduces two novel choices of step-size parameters, leading to efficient descent directions…

The optimal robot assembly planning problem is challenging due to the necessity of finding the optimal solution amongst an exponentially vast number of possible plans, all while satisfying a selection of constraints. Traditionally, robotic…

We present a principled approach for estimating the matrix of microscopic rates among states of a Markov process, given only its stationary state population distribution and a single average global kinetic observable. We adapt Maximum…