Nonlinear Analysis and Optimization with Applications

Nonlinear analysis has wide and significant applications in many areas of mathematics, including functional analysis, variational analysis, nonlinear optimization, convex analysis, nonlinear ordinary and partial differential equations, dynamical system theory, mathematical economics, game theory, signal processing, control theory, data mining, and so forth. Optimization problems have been intensively investigated, and various feasible methods in analyzing convergence of algorithms have been developed over the last half century. In this Special Issue, we will focus on the connection between nonlinear analysis and optimization as well as their applications to integrate basic science into the real world

Fast Stochastic Surrogate Modeling via Rational Polynomial Chaos Expansions and Principal Component Analysis

This paper introduces a fast stochastic surrogate modeling technique for the frequency-domain responses of linear and passive electrical and electromagnetic systems based on polynomial chaos expansion (PCE) and principal component analysis (PCA). A rational PCE model provides high accuracy, whereas the PCA allows compressing the model, leading to a reduced number of coefficients to estimate and thereby improving the overall training efficiency. Furthermore, the PCA compression is shown to provide additional accuracy improvements thanks to its intrinsic regularization properties. The effectiveness of the proposed method is illustrated by means of several application examples

System- and Data-Driven Methods and Algorithms

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This first volume focuses on real-time control theory, data assimilation, real-time visualization, high-dimensional state spaces and interaction of different reduction techniques

Fast Stochastic Surrogate Modeling via Rational Polynomial Chaos Expansions and Principal Component Analysis

This paper introduces a fast stochastic surrogate modeling technique for the frequency-domain responses of linear and passive electrical and electromagnetic systems based on polynomial chaos expansion (PCE) and principal component analysis (PCA). A rational PCE model provides high accuracy, whereas the PCA allows compressing the model, leading to a reduced number of coefficients to estimate and thereby improving the overall training efficiency. Furthermore, the PCA compression is shown to provide additional accuracy improvements thanks to its intrinsic regularization properties. The effectiveness of the proposed method is illustrated by means of several application examples

7th International Conference on Nonlinear Vibrations, Localization and Energy Transfer: Extended Abstracts

International audienceThe purpose of our conference is more than ever to promote exchange and discussions between scientists from all around the world about the latest research developments in the area of nonlinear vibrations, with a particular emphasis on the concept of nonlinear normal modes and targeted energytransfer

Model Order Reduction

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This three-volume handbook covers methods as well as applications. This third volume focuses on applications in engineering, biomedical engineering, computational physics and computer science

Meta-Modelling of Intensive Computational Models

Engineering process design for applications that use computationally intensive nonlinear dynamical systems can be expensive in time and resources. The presented work reviews the concept of a meta-model as a way to improve the efficiency of this process. The proposed meta-model will have a computational advantage in implementation over the computationally intensive model therefore reducing the time and resources required to design an engineering process. This work proposes to meta-model a computationally intensive nonlinear dynamical system using reduced-order linear parameter varying system modelling approach with local linear models in velocity based linearization form. The parameters of the linear time-varying meta-model are blended using Gaussian Processes regression models. The meta-model structure is transparent and relates directly to the dynamics of the computationally intensive model while the velocity-based local linear models faithfully reproduce the original system dynamics anywhere in the operating space of the system. The non-parametric blending of the meta-model local linear models by Gaussian Processes regression models is ideal to deal with data sparsity and will provide uncertainty information about the meta-model predictions. The proposed meta-model structure has been applied to second-order nonlinear dynamical systems, a small sized nonlinear transmission line model, medium sized fluid dynamics problem and the computationally intensive nonlinear transmission line model of order 5000