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Density ratio estimation is fundamental to tasks involving $f$-divergences, yet existing methods often fail under significantly different distributions or inadequately overlapping supports -- the density-chasm and the support-chasm…
This paper presents a minimum flow approach applicable to a wide range of doubly nonlinear diffusion problems. We introduce a minimum flow steepest descent algorithm that seeks an optimal traffic flow by minimizing an internal energy…
We develop a fast divided-and-conquer indirect collocation method for the homogeneous Dirichlet boundary value problem of variable-order space-fractional diffusion equations. Due to the impact of the space-dependent variable order, the…
We have developed an adaptive structural Deep Belief Network (Adaptive DBN) that finds an optimal network structure in a self-organizing manner during learning. The Adaptive DBN is the hierarchical architecture where each layer employs…
Numerous diffusion model (DM)-based methods have been proposed for solving inverse imaging problems. Among these, a recent line of work has demonstrated strong performance by formulating sampling as an optimization procedure that enforces…
Deep convolutional neural networks (DCNN) have been widely adopted for research on super resolution recently, however previous work focused mainly on stacking as many layers as possible in their model, in this paper, we present a new…
A deep learning approach to blind denoising of images without complete knowledge of the noise statistics is considered. We propose DN-ResNet, which is a deep convolutional neural network (CNN) consisting of several residual blocks…
A new model order reduction approach is proposed for parametric steady-state nonlinear fluid flows characterized by shocks and discontinuities whose spatial locations and orientations are strongly parameter dependent. In this method,…
We consider a singularly perturbed reaction diffusion problem as a first order two-by-two system. Using piecewise discontinuous polynomials for the first component and $H_{div}$-conforming elements for the second component we provide a…
Diffusion Probabilistic Models (DPMs) have recently shown remarkable performance in image generation tasks, which are capable of generating highly realistic images. When adopting DPMs for image restoration tasks, the crucial aspect lies in…
In recent advancements in high-fidelity image generation, Denoising Diffusion Probabilistic Models (DDPMs) have emerged as a key player. However, their application at high resolutions presents significant computational challenges. Current…
We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving empirical risk minimization (ERM) problems with a nonsmooth regularization term. Our algorithm is applicable…
The single image super-resolution task is one of the most examined inverse problems in the past decade. In the recent years, Deep Neural Networks (DNNs) have shown superior performance over alternative methods when the acquisition process…
In this paper, we develop an efficient numerical solver for unsteady diffusion-type partial differential equations with random coefficients. A major computational challenge in such problems lies in repeatedly handling large-scale linear…
Diffusion bridge models establish probabilistic paths between arbitrary paired distributions and exhibit great potential for universal image restoration. Most existing methods merely treat them as simple variants of stochastic interpolants,…
In the context of continuously rising global air traffic, efficient and safe Conflict Detection and Resolution (CD&R) is paramount for air traffic management. Although Deep Reinforcement Learning (DRL) offers a promising pathway for CD&R…
Diffusion tensor imaging (DTI) holds significant importance in clinical diagnosis and neuroscience research. However, conventional model-based fitting methods often suffer from sensitivity to noise, leading to decreased accuracy in…
In this paper, we consider a class of discontinuous Galerkin (DG) methods for one-dimensional nonlocal diffusion (ND) problems. The nonlocal models, which are integral equations, are widely used in describing many physical phenomena with…
The solution of nonsymmetric but positive definite (NSPD) systems arising from advection-diffusion problems is an important research topic in science and engineering. Balancing domain decomposition by constraints with an adaptive coarse…
The power budget for embedded hardware implementations of Deep Learning algorithms can be extremely tight. To address implementation challenges in such domains, new design paradigms, like Approximate Computing, have drawn significant…