scholarly journals Non-intrusive model reduction of large-scale, nonlinear dynamical systems using deep learning

2020 ◽  
Vol 412 ◽  
pp. 132614
Author(s):  
Han Gao ◽  
Jian-Xun Wang ◽  
Matthew J. Zahr
Keyword(s):  
Deep Learning ◽  
Dynamical Systems ◽  
Model Reduction ◽  
Large Scale ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical

Large-Scale Impulsive Dynamical Systems

2011 ◽  
Author(s):  
Wassim M. Haddad ◽  
Sergey G. Nersesov
Keyword(s):  
Dynamical Systems ◽  
Lyapunov Functions ◽  
Large Scale ◽  
Nonlinear Dynamical Systems ◽  
Supply Rate ◽  
Nonlinear Dynamical ◽  
Dissipation Inequality ◽  
Vector Lyapunov Functions ◽  
Definition Of ◽  
Stability Results

This chapter develops vector dissipativity notions for large-scale nonlinear impulsive dynamical systems. In particular, it introduces a generalized definition of dissipativity for large-scale nonlinear impulsive dynamical systems in terms of a hybrid vector dissipation inequality involving a vector hybrid supply rate, a vector storage function, and an essentially nonnegative, semistable dissipation matrix. The chapter also defines generalized notions of a vector available storage and a vector required supply and shows that they are element-by-element ordered, nonnegative, and finite. Extended Kalman-Yakubovich-Popov conditions, in terms of the local impulsive subsystem dynamics and the interconnection constraints, are developed for characterizing vector dissipativeness via vector storage functions for large-scale impulsive dynamical systems. Finally, using the concepts of vector dissipativity and vector storage functions as candidate vector Lyapunov functions, the chapter presents feedback interconnection stability results of large-scale impulsive nonlinear dynamical systems.

scholarly journals The Brain Dynamics Toolbox for Matlab

2017 ◽  
Author(s):  
Stewart Heitmann ◽  
Matthew J Aburn ◽  
Michael Breakspear
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Computational Neuroscience ◽  
Large Scale ◽  
Nonlinear Dynamical Systems ◽  
Brain Dynamics ◽  
Interactive Simulation ◽  
Nonlinear Dynamical ◽  
Delay Differential ◽  
The Brain

AbstractNonlinear dynamical systems are increasingly informing both theoretical and empirical branches of neuroscience. The Brain Dynamics Toolbox provides an interactive simulation platform for exploring such systems in MATLAB. It supports the major classes of differential equations that arise in computational neuroscience: Ordinary Differential Equations, Delay Differential Equations and Stochastic Differential Equations. The design of the graphical interface fosters intuitive exploration of the dynamics while still supporting scripted parameter explorations and large-scale simulations. Although the toolbox is intended for dynamical models in computational neuroscience, it can be applied to dynamical systems from any domain.

scholarly journals Artificial Intelligence, Chaos, Prediction and Understanding in Science

2021 ◽  
Vol 31 (11) ◽  
pp. 2150173
Author(s):  
Miguel A. F. Sanjuán
Keyword(s):  
Artificial Intelligence ◽  
Machine Learning ◽  
Big Data ◽  
Deep Learning ◽  
Dynamical Systems ◽  
Chaotic Dynamics ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical ◽  
Constructive Dialogue ◽  
Learning Techniques

Machine learning and deep learning techniques are contributing much to the advancement of science. Their powerful predictive capabilities appear in numerous disciplines, including chaotic dynamics, but they miss understanding. The main thesis here is that prediction and understanding are two very different and important ideas that should guide us to follow the progress of science. Furthermore, the important role played by nonlinear dynamical systems is emphasized for the process of understanding. The path of the future of science will be marked by a constructive dialogue between big data and big theory, without which we cannot understand.

A new model reduction method for nonlinear dynamical systems

2009 ◽  
Vol 59 (1-2) ◽  
pp. 183-194 ◽  
Author(s):  
Nikolaos Kazantzis ◽  
Costas Kravaris ◽  
Lemonia Syrou
Keyword(s):  
Dynamical Systems ◽  
Model Reduction ◽  
Reduction Method ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical ◽  
New Model
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