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With the rapid development of diffusion models and flow-based generative models, there has been a surge of interests in solving noisy linear inverse problems, e.g., super-resolution, deblurring, denoising, colorization, etc, with generative…

Machine Learning · Computer Science 2024-10-22 Xiangming Meng , Yoshiyuki Kabashima

Modern diffusion models, particularly those utilizing a Transformer-based UNet for denoising, rely heavily on self-attention operations to manage complex spatial relationships, thus achieving impressive generation performance. However, this…

Computer Vision and Pattern Recognition · Computer Science 2024-10-18 Songhua Liu , Weihao Yu , Zhenxiong Tan , Xinchao Wang

Diffusion-based inpainting can reconstruct missing image areas with high quality from sparse data, provided that their location and their values are well optimised. This is particularly useful for applications such as image compression,…

Image and Video Processing · Electrical Eng. & Systems 2023-03-24 Pascal Peter , Karl Schrader , Tobias Alt , Joachim Weickert

This work aims to improve the applicability of diffusion models in realistic image restoration. Specifically, we enhance the diffusion model in several aspects such as network architecture, noise level, denoising steps, training image size,…

Computer Vision and Pattern Recognition · Computer Science 2023-04-18 Ziwei Luo , Fredrik K. Gustafsson , Zheng Zhao , Jens Sjölund , Thomas B. Schön

We present a distributed quasi-Newton (DQN) method, which enables a group of agents to compute an optimal solution of a separable multi-agent optimization problem locally using an approximation of the curvature of the aggregate objective…

Optimization and Control · Mathematics 2024-09-30 Ola Shorinwa , Mac Schwager

Denoising diffusion probabilistic models (DDPMs) have achieved impressive performance on various image generation tasks, including image super-resolution. By learning to reverse the process of gradually diffusing the data distribution into…

Image and Video Processing · Electrical Eng. & Systems 2023-07-25 Kai Zhao , Alex Ling Yu Hung , Kaifeng Pang , Haoxin Zheng , Kyunghyun Sung

We extend to multi-dimensions the work of [1], where new fully explicit kinetic methods were built for the approximation of linear and non-linear convection-diffusion problems. The fundamental principles from the earlier work are retained:…

Numerical Analysis · Mathematics 2023-12-29 Gauthier Wissocq , Rémi Abgrall

An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents…

Numerical Analysis · Mathematics 2018-02-07 Camille Negrello , Pierre Gosselet , Christian Rey

This work develops robust diffusion recursive least squares algorithms to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. The first algorithm minimizes an exponentially…

Machine Learning · Computer Science 2019-02-05 Y. Yu , H. Zhao , R. C. de Lamare , Y. Zakharov , L. Lu

The ground state energy of a many-electron system can be approximated by an variational approach in which the total energy of the system is minimized with respect to one and two-body reduced density matrices (RDM) instead of many-electron…

Optimization and Control · Mathematics 2017-09-01 Yongfeng Li , Zaiwen Wen , Chao Yang , Yaxiang Yuan

The online 3D bin packing problem is important in logistics, warehousing and intelligent manufacturing, with solutions shifting to deep reinforcement learning (DRL) which faces challenges like low sample efficiency. This paper proposes a…

Robotics · Computer Science 2026-04-14 Jie Han , Tong Li , Qingyang Xu , Yong Song , Bao Pang , Xianfeng Yuan

Optimal control of diffusion processes is intimately connected to the problem of solving certain Hamilton-Jacobi-Bellman equations. Building on recent machine learning inspired approaches towards high-dimensional PDEs, we investigate the…

Optimization and Control · Mathematics 2023-01-31 Nikolas Nüsken , Lorenz Richter

We present a fast direct solution method for the advection-diffusion equation in one and two dimensions with non-periodic boundaries. Computational cost is reduced to $\mathcal O(N)$ by making a low-rank approximation of the Green's…

Computational Physics · Physics 2016-12-30 Jonathan R. Bull

Fluid-structure interaction models are used to study how a material interacts with different fluids at different Reynolds numbers. Examining the same model not only for different fluids but also for different solids allows to optimize the…

Numerical Analysis · Mathematics 2023-07-28 Peter Benner , Thomas Richter , Roman Weinhandl

The design of multitarget rendezvous missions requires a method to quickly and accurately approximate the optimal transfer between any two rendezvous targets. In this paper, a deep neural network (DNN)-based method is proposed for quickly…

Optimization and Control · Mathematics 2019-02-26 Yue-he Zhu , Ya-zhong Luo

The classical Ka\v{c}anov scheme for the solution of nonlinear variational problems can be interpreted as a fixed point iteration method that updates a given approximation by solving a linear problem in each step. Based on this observation,…

Numerical Analysis · Mathematics 2021-11-30 Pascal Heid , Thomas P. Wihler

This paper considers a nested stochastic distributed optimization problem. In it, approximate solutions to realizations of the inner-problem are leveraged to obtain a Distributed Stochastic Cubic Regularized Newton (DiSCRN) update to the…

Optimization and Control · Mathematics 2021-08-06 Tor Anderson , Sonia Martinez

We study distributed optimization problems over multi-agent networks, including consensus and network flow problems. Existing distributed methods neglect the heterogeneity among agents' computational capabilities, limiting their…

Optimization and Control · Mathematics 2023-08-03 Xiaochun Niu , Ermin Wei

Currently, methods for single-image deblurring based on CNNs and transformers have demonstrated promising performance. However, these methods often suffer from perceptual limitations, poor generalization ability, and struggle with heavy or…

Computer Vision and Pattern Recognition · Computer Science 2025-03-11 Xiaoyang Liu , Yuquan Wang , Zheng Chen , Jiezhang Cao , He Zhang , Yulun Zhang , Xiaokang Yang

In this study, we present the numerical investigation of the Dirichlet-Neumann Waveform Relaxation (DNWR) algorithm applied to multiple subdomains for the reaction-diffusion equation with time delay. Various arrangements of transmission…

Numerical Analysis · Mathematics 2026-02-16 Bankim C. Mandal , Deeksha Tomer