Neural Networks for Modeling and Controlling Dynamical Systems

2001 ◽  
pp. 81-96
Author(s):  
Luigi Fortuna ◽  
Gianguido Rizzotto ◽  
Mario Lavorgna ◽  
Giuseppe Nunnari ◽  
M. Gabriella Xibilia ◽  
...  
Keyword(s):  
Neural Networks ◽  
Dynamical Systems

Nonlinear reduction of high-dimensional dynamical systems via neural networks

1994 ◽  
Vol 72 (12) ◽  
pp. 1822-1825 ◽  
Author(s):  
Michael Kirby ◽  
Rick Miranda
Keyword(s):  
Neural Networks ◽  
Dynamical Systems ◽  
High Dimensional

scholarly journals Simulating and Predicting Dynamical Systems with Spatial Semantic Pointers

2021 ◽  
pp. 1-35
Author(s):  
Aaron R. Voelker ◽  
Peter Blouw ◽  
Xuan Choo ◽  
Nicole Sandra-Yaffa Dumont ◽  
Terrence C. Stewart ◽  
...  
Keyword(s):  
Neural Networks ◽  
Dynamical Systems ◽  
Cognitive Processes ◽  
Deep Neural Networks ◽  
Learning Task ◽  
Topological Spaces ◽  
Multiple Objects ◽  
Symbolic Structure ◽  
High Level ◽  
Vector Representations

Abstract While neural networks are highly effective at learning task-relevant representations from data, they typically do not learn representations with the kind of symbolic structure that is hypothesized to support high-level cognitive processes, nor do they naturally model such structures within problem domains that are continuous in space and time. To fill these gaps, this work exploits a method for defining vector representations that bind discrete (symbol-like) entities to points in continuous topological spaces in order to simulate and predict the behavior of a range of dynamical systems. These vector representations are spatial semantic pointers (SSPs), and we demonstrate that they can (1) be used to model dynamical systems involving multiple objects represented in a symbol-like manner and (2) be integrated with deep neural networks to predict the future of physical trajectories. These results help unify what have traditionally appeared to be disparate approaches in machine learning.

Dynamics of Neural Networks as Nonlinear Systems with Several Equilibria

2011 ◽  
pp. 331-357 ◽  
Author(s):  
Daniela Danciu
Keyword(s):  
Neural Network ◽  
Dynamical System ◽  
Neural Networks ◽  
Time Delay ◽  
Dynamical Systems ◽  
Qualitative Properties ◽  
The Neural Network ◽  
The Neural Networks ◽  
Global Asymptotics ◽  
Dynamical Properties

Neural networks—both natural and artificial, are characterized by two kinds of dynamics. The first one is concerned with what we would call “learning dynamics”. The second one is the intrinsic dynamics of the neural network viewed as a dynamical system after the weights have been established via learning. The chapter deals with the second kind of dynamics. More precisely, since the emergent computational capabilities of a recurrent neural network can be achieved provided it has suitable dynamical properties when viewed as a system with several equilibria, the chapter deals with those qualitative properties connected to the achievement of such dynamical properties as global asymptotics and gradient-like behavior. In the case of the neural networks with delays, these aspects are reformulated in accordance with the state of the art of the theory of time delay dynamical systems.

Applications of neural networks in learning of dynamical systems

1992 ◽  
Vol 22 (1) ◽  
pp. 161-164 ◽  
Author(s):  
S.R. Chu ◽  
R. Shoureshi
Keyword(s):  
Neural Networks ◽  
Dynamical Systems
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