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An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and…
Deep learning has been employed to identify flow characteristics from Computational Fluid Dynamics (CFD) databases to assist the researcher to better understand the flow field, to optimize the geometry design and to select the correct CFD…
Finding latent structures in data is drawing increasing attention in diverse fields such as image and signal processing, fluid dynamics, and machine learning. In this work we examine the problem of finding the main modes of gradient flows.…
Foundations of a new projection-based model reduction approach for convection dominated nonlinear fluid flows are summarized. In this method the evolution of the flow is approximated in the Lagrangian frame of reference. Global basis…
The Gradient Vector Flow (GVF) is a vector diffusion approach based on Partial Differential Equations (PDEs). This method has been applied together with snake models for boundary extraction medical images segmentation. The key idea is to…
We introduce a generic scheme to solve nonconvex optimization problems using gradient-based algorithms originally designed for minimizing convex functions. Even though these methods may originally require convexity to operate, the proposed…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
In this paper, we consider the problem of system identification when side-information is available on the steady-state (or DC) gain of the system. We formulate a general nonparametric identification method as an infinite-dimensional…
In this paper we derive nonlinear evolution equations associated with a class of non-convex energy functionals which can be used for correcting displacement errors in imaging data. We study properties of these filtering flows and provide…
In this paper, acceleration of gradient methods for convex optimization problems with weak levels of convexity and smoothness is considered. Starting from the universal fast gradient method which was designed to be an optimal method for…
This paper is concerned with the optimal shape design of the newtonian viscous incompressible fluids driven by the stationary nonhomogeneous Navier-Stokes equations. We use three approaches to derive the structures of shape gradients for…
A parabolic system of three unknown functions, not expressible as gradient flows, is treated as three coupled gradient flows. For each unknown function, the minimizing movement scheme is used to construct a time-discrete approximate…
In the field of machine learning, comprehending the intricate training dynamics of neural networks poses a significant challenge. This paper explores the training dynamics of neural networks, particularly whether these dynamics can be…
This paper proposes a convex optimization based method that either locates all real roots of a set of power flow equations or declares no real solution exists in the given area. In the proposed method, solving the power flow equations is…
The phase retrieval problem has garnered significant attention since the development of the PhaseLift algorithm, which is a convex program that operates in a lifted space of matrices. Because of the substantial computational cost due to…
Wasserstein gradient flow has emerged as a promising approach to solve optimization problems over the space of probability distributions. A recent trend is to use the well-known JKO scheme in combination with input convex neural networks to…
We present an efficient deep learning technique for the model reduction of the Navier-Stokes equations for unsteady flow problems. The proposed technique relies on the Convolutional Neural Network (CNN) and the stochastic gradient descent…
In the field of fluid numerical analysis, there has been a long-standing problem: lacking of a rigorous mathematical tool to map from a continuous flow field to discrete vortex particles, hurdling the Lagrangian particles from inheriting…
Optimal control of turbulent mixed-convection flows has attracted considerable attention from researchers. Numerical algorithms such as Genetic Algorithms (GAs) are powerful tools that allow to perform global optimization. These algorithms…
Despite the widespread use of gradient-based algorithms for optimizing high-dimensional non-convex functions, understanding their ability of finding good minima instead of being trapped in spurious ones remains to a large extent an open…