Related papers: Windowing Regularization Techniques for Unsteady A…

Aerodynamic optimization is ubiquitous in the design of most engineering systems interacting with fluids. A common approach is to optimize a performance function defined by a choice of an aerodynamic model, e.g., turbulence RANS model, and…

Most fluid flow problems that are vital in engineering applications involve at least one of the following features: turbulence, shocks, and/or material interfaces. While seemingly different phenomena, these flows all share continuous…

During the inversion of discrete linear systems noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during…

Matrix-valued optimization tasks, including those involving symmetric positive definite (SPD) matrices, arise in a wide range of applications in machine learning, data science and statistics. Classically, such problems are solved via…

A novel method to estimate unsteady aerodynamic force coefficients from pointwise velocity measurements is presented. The methodology is based on a resolvent-based reduced-order model which requires the mean flow to obtain physical flow…

Data assimilation (DA) plays a crucial role in extracting valuable information from flow measurements in fluid dynamics problems. Often only time-averaged data is available, which poses challenges for DA in the context of unsteady flow…

Probabilistic forecasting of multivariate time series is essential for various downstream tasks. Most existing approaches rely on the sequences being uniformly spaced and aligned across all variables. However, real-world multivariate time…

Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…

In most practical applications such as recommendation systems, display advertising, and so forth, the collected data often contains missing values and those missing values are generally missing-not-at-random, which deteriorates the…

Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…

We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…

Inspired by the adaptation phenomenon of neuronal firing, we propose the regularity normalization (RN) as an unsupervised attention mechanism (UAM) which computes the statistical regularity in the implicit space of neural networks under the…

Adaptive cubic regularization methods have emerged as a credible alternative to linesearch and trust-region for smooth nonconvex optimization, with optimal complexity amongst second-order methods. Here we consider a general/new class of…

This paper examines an averaging technique in which the nonlinear flux term is expanded and the convective velocities are passed through a low-pass filter. It is the intent that this modification to the nonlinear flux terms will result in…

Since the 1990s, RANS practitioners have observed spontaneous unsteadiness in RANS simulations. Some have suggested deliberately using this as a method of resolving large turbulent structures. However, to date, no one has produced a…

In order to tackle the difficulty associated with the ill-posed nature of the image registration problem, regularization is often used to constrain the solution space. For most learning-based registration approaches, the regularization…

Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…

With more efficient structures, last trends in aeronautics have witnessed an increased flexibility of wings, calling for adequate design and optimization approaches. To correctly model the coupled physics, aerostructural optimization has…

Regularization is a powerful technique for extracting useful information from noisy data. Typically, it is implemented by adding some sort of norm constraint to an objective function and then exactly optimizing the modified objective…

We investigate the prediction of the turbulent flow around a canonical square cylinder at Re= 22000 solving the unsteady Reynolds-averaged Navier-Stokes (URANS) equations. The limitations of URANS modelling are overcome through the…