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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…
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…
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,…
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,…
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…
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…
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:…
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…
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…
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…
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…
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…
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…
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…
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…
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,…
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…
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…
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…
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…