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Exponential decay estimates of a general linear weakly damped wave equation are studied with decay rate lying in a range. Based on the $C^0$-conforming finite element method to discretize spatial variables keeping temporal variable…
This study focuses on using direct methods (first-discretize-then-optimize) to solve optimal control problems for a class of nonsmooth dynamical systems governed by differential variational inequalities (DVI), called optimal control…
The Virtual Element Method (VEM) is a novel family of numerical methods for approximating partial differential equations on very general polygonal or polyhedral computational grids. This work aims to propose a Balancing Domain Decomposition…
This article investigates the numerical approximation of shape optimization problems with PDE constraint on classes of convex domains. The convexity constraint provides a compactness property which implies well posedness of the problem.…
An original approach, termed Divide-and-Evolve is proposed to hybridize Evolutionary Algorithms (EAs) with Operational Research (OR) methods in the domain of Temporal Planning Problems (TPPs). Whereas standard Memetic Algorithms use local…
We consider compact finite-difference schemes of the 4th approximation order for an initial-boundary value problem (IBVP) for the $n$-dimensional non-homogeneous wave equation, $n\geq 1$. Their construction is accomplished by both the…
Partial differential equations (PDEs) form a central component of scientific computing. Among recent advances in deep learning, evolutionary neural networks have been developed to successively capture the temporal dynamics of time-dependent…
Evolutionary computation offers a variety of tools to solve complex real-world optimization problems. However, research often focuses on smaller, simplified problems and optimization algorithms that sometimes miss expectations in real-world…
The paper deals with the optimal control problem described by second order evolution differential inclusions; to this end first we use an auxiliary problem with second order discrete and discrete-approximate inclusions. Then applying…
We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested…
In this paper, we introduce an efficient method for computing curves minimizing a variant of the Euler-Mumford elastica energy, with fixed endpoints and tangents at these endpoints, where the bending energy is enhanced with a user defined…
Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant…
The problem of partial null controllability for linear autonomous evolution equations, which are controlled by a one-dimensional control, is under consideration. The partial null-controllability conditions for coupled abstract evolution…
In this paper, an enhanced unified differential evolution algorithm, named UDE-III, is presented for real parameter-constrained optimization problems (COPs). The proposed UDE-III is a significantly enhanced version of the Improved UDE…
We consider the primal and dual forms of the optimality conditions for PDE-contrained optimization problems arising in Data-Driven Computational Mechanics when specialized to the reaction-diffusion context. Starting with the continuous…
The use of Evolutionary Algorithms (EA) for solving Mathematical/Computational Optimization Problems is inspired by the biological processes of Evolution. Few of the primitives involved in the Evolutionary process/paradigm are selection of…
Support vector machine (SVM) is a powerful machine learning algorithm to handle classification tasks. However, the classical SVM is developed for binary problems with the assumption of balanced datasets. Obviously, the multi-class…
In this paper we consider fully discrete approximations of abstract evolution equations, by means of a quasi non-conforming spatial approximation and finite differences in time (Rothe-Galerkin method). The main result is the convergence of…
We study a class of stochastic evolution equations of jump type with random coefficients and its optimal control problem. There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous…
This paper proposes the Nerual Energy Descent (NED) via neural network evolution equations for a wide class of deep learning problems. We show that deep learning can be reformulated as the evolution of network parameters in an evolution…