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In this paper, we propose improved wall-treatment strategies for meshfree methods applied to turbulent flows. The goal is to enhance wall-function handling in simulations of high-Reynolds-number turbulent flows and to understand the…
We propose a distributed algorithm for solving the optimization problem Basis Pursuit (BP). BP finds the least L1-norm solution of the underdetermined linear system Ax = b and is used, for example, in compressed sensing for reconstruction.…
Recently, many studies have shed light on the high adaptivity of deep neural network methods in nonparametric regression models, and their superior performance has been established for various function classes. Motivated by this…
Approximation of scattered geometric data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This method is useful for…
Image denoising is a fundamental problem in computational photography, where achieving high perception with low distortion is highly demanding. Current methods either struggle with perceptual quality or suffer from significant distortion.…
This work proposes a distributed algorithm for solving empirical risk minimization problems, called L-DQN, under the master/worker communication model. L-DQN is a distributed limited-memory quasi-Newton method that supports asynchronous…
We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…
We present a novel communication-efficient Newton-type algorithm for finite-sum optimization over a distributed computing environment. Our method, named DINO, overcomes both theoretical and practical shortcomings of similar existing…
Chemically reacting flows are common in engineering, such as hypersonic flow, combustion, explosions, manufacturing processes and environmental assessments. For combustion, the number of reactions can be significant (over 100) and due to…
In Part I of this work, we have proposed a general framework of decentralized stochastic quasi-Newton methods, which converge linearly to the optimal solution under the assumption that the local Hessian inverse approximations have bounded…
Diffusion-induced Ramsey narrowing that appears when atoms can leave the interaction region and repeatedly return without lost of coherence is investigated using strong collisions approximation. The effective diffusion equation is obtained…
A least-squares neural network (LSNN) method was introduced for solving scalar linear and nonlinear hyperbolic conservation laws (HCLs) in [7, 6]. This method is based on an equivalent least-squares (LS) formulation and uses ReLU neural…
Diffusion Schr\"odinger bridges (DSB) have recently emerged as a powerful framework for recovering stochastic dynamics via their marginal observations at different time points. Despite numerous successful applications, existing algorithms…
This article investigates a local discontinuous Galerkin (LDG) method for one-dimensional and two-dimensional singularly perturbed reaction-diffusion problems on a Shishkin mesh. During this process, due to the inability of the energy norm…
The application of the diffusion in many computer vision and artificial intelligence projects has been shown to give excellent improvements in performance. One of the main bottlenecks of this technique is the quadratic growth of the kNN…
This paper develops an approach for solving perpetual discounted optimal stopping problems for multidimensional diffusions, with special emphasis on the $d$-dimensional Wiener process. We first obtain some verification theorems for…
Strang splitting is a widely used second-order method for solving diffusion-reaction problems. However, its convergence order is often reduced to order $1$ for Dirichlet boundary conditions and to order $1.5$ for Neumann and Robin boundary…
Batch Normalization (BN) has been proven to be quite effective at accelerating and improving the training of deep neural networks (DNNs). However, BN brings additional computation, consumes more memory and generally slows down the training…
Beam alignment is a key challenge in directional mmWave and THz systems, where narrow beams require accurate yet low-overhead training. Existing learning-based approaches typically predict a single beam and do not quantify uncertainty,…
Recent research works for solving partial differential equations (PDEs) with deep neural networks (DNNs) have demonstrated that spatiotemporal function approximators defined by auto-differentiation are effective for approximating nonlinear…