相关论文: Statistical Mechanics of Hamiltonian Adaptive Reso…

This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. The proposed procedure has several features which distinguishes it from the other procedures for the problem. First of all a sliding…

In this paper, we consider an unconstrained optimization model where the objective is a sum of a large number of possibly nonconvex functions, though overall the objective is assumed to be smooth and convex. Our bid to solving such model…

We present a new multigrid scheme for solving the Poisson equation with Dirichlet boundary conditions on a Cartesian grid with irregular domain boundaries. This scheme was developed in the context of the Adaptive Mesh Refinement (AMR)…

In this paper, a stochastic alternating direction method of multipliers (ADMM) is proposed for a class of nonsmooth composite and stochastic convex optimization problems in Hilbert space, motivated by optimization problems constrained by…

Parallel trajectory optimization via the Alternating Direction Method of Multipliers (ADMM) has emerged as a scalable approach to long-horizon motion planning. However, existing frameworks typically decompose the problem into parallel…

We introduce Adjoint Sampling, a highly scalable and efficient algorithm for learning diffusion processes that sample from unnormalized densities, or energy functions. It is the first on-policy approach that allows significantly more…

It is proposed to apply modern methods of nonlinear nonequilibrium statistical mechanics to develop software algorithms that will optimally respond to targets within short response times with minimal computer resources. This Statistical…

While adaptive sensing has provided improved rates of convergence in sparse regression and classification, results in nonparametric regression have so far been restricted to quite specific classes of functions. In this paper, we describe an…

A theoretical scheme for the treatment of an open molecular system with electrons and nuclei is proposed. The idea is based on the Grand Canonical description of a quantum region embedded in a classical reservoir of molecules. Electronic…

This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic…

Heterogeneous multi-robot systems (HMRS) have emerged as a powerful approach for tackling complex tasks that single robots cannot manage alone. Current large-language-model-based multi-agent systems (LLM-based MAS) have shown success in…

We discuss our new implementation of the Real-space Electronic Structure method for studying the atomic and electronic structure of infinite periodic as well as finite systems, based on density functional theory. This improved version which…

Alternating Direction Method of Multipliers (ADMM) is a popular method for solving large-scale Machine Learning problems. Stochastic ADMM was proposed to reduce the per iteration computational complexity, which is more suitable for big data…

We proposed a novel dense line spectrum super-resolution algorithm, the DMRA, that leverages dynamical multi-resolution of atoms technique to address the limitation of traditional compressed sensing methods when handling dense point-source…

Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…

Within recent years, considerable progress has been made regarding high-performance solvers for Partial Differential Equations (PDEs), yielding potential gains in efficiency compared to industry standard tools. However, the latter largely…

Convolutional neural networks can automatically learn features via deep network architectures and given input samples. However, the robustness of obtained models may face challenges in varying scenes. Bigger differences in network…

Randomized Smoothing (RS) is considered the state-of-the-art approach to obtain certifiably robust models for challenging tasks. However, current RS approaches drastically decrease standard accuracy on unperturbed data, severely limiting…

Stochastic variance reduced optimization methods are known to be globally convergent while they suffer from slow local convergence, especially when moderate or high accuracy is needed. To alleviate this problem, we propose an optimization…

Obtainable computational efficiency is evaluated when using an Adaptive Mesh Refinement (AMR) strategy in time accurate simulations governed by sets of conservation laws. For a variety of 1D, 2D, and 3D hydro- and magnetohydrodynamic…