Estimating Invariant Sets using Physics-Informed Neural Networks

2022 ◽  
Author(s):  
Venkata Vaishnav Tadiparthi ◽  
Raktim Bhattacharya
Keyword(s):  
Neural Networks ◽  
Invariant Sets

scholarly journals Attracting and Quasi-Invariant Sets of Cohen-Grossberg Neural Networks with Time Delay in the Leakage Term under Impulsive Perturbations

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Guiying Chen ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Differential Inequality ◽  
Invariant Sets ◽  
Leakage Term ◽  
Impulsive Perturbations ◽  
Delay Differential ◽  
Delay Differential Inequality

A class of impulsive Cohen-Grossberg neural networks with time delay in the leakage term is investigated. By using the method ofM-matrix and the technique of delay differential inequality, the attracting and invariant sets of the networks are obtained. The results in this paper extend and improve the earlier publications. An example is presented to illustrate the effectiveness of our conclusion.

Complete Stability in Multistable Delayed Neural Networks

2009 ◽  
Vol 21 (3) ◽  
pp. 719-740 ◽  
Author(s):  
Chang-Yuan Cheng ◽  
Chih-Wen Shih
Keyword(s):  
Neural Networks ◽  
Dynamical Property ◽  
Invariant Sets ◽  
Numerical Illustration ◽  
Neuron System ◽  
Delayed Neural Networks ◽  
New Formulation ◽  
Positively Invariant Sets

We investigate the complete stability for multistable delayed neural networks. A new formulation modified from the previous studies on multistable networks is developed to derive componentwise dynamical property. An iteration argument is then constructed to conclude that every solution of the network converges to a single equilibrium as time tends to infinity. The existence of 3n equilibria and 2n positively invariant sets for the n-neuron system remains valid under the new formulation. The theory is demonstrated by a numerical illustration.

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