Nonlinearity and Information Processing
Abstract
Artificial neural networks can approximate functions, model dynamics and beat human grand masters at chess and Go. However, they usually require very many high-quality training examples, which might be experimentally hard to obtain. Physics-informed neural networks mitigate this problem by encoding some kind of fundamental physics bias, such as time-invariance symmetry or, in our proposed work, knowledge of nonlinear dynamics and chaos.We propose to systematically train conventional and Hamiltonian neural networks on increasingly difficult dynamical systems as well as implementing such networks upon conventional and chaotic (Chaogate Based) computational systems. We propose to investigate understand and elucidate how such novel neural networks (such as Hamiltonian Neural Networks,Generalized Hamiltonian Neural Networks, Chaogate based Neural Networks) can learn and behave differently from conventional neural networks. In particular, we will focus upon exploiting chaos for learning and forecasting in high-dimensional systems. We propose tosystematically vary the dimension of the higher dimensional systems and the amount of training data while measuring the performanceof a Chaos Aware and Chaogate Based Neural Networks. Viewing this work in the larger context of machine learning underscores its potential impact to enable us to develop Chaos Based/Aware Artificial Intelligence Systems that are both knowledgeable of chaotic dynamics but also exploit that knowledge to exploit or base its performance upon the rich complexities inherent to nonlinear dynamical systems. We also propose to investigate how neuronal diversity and nonlinearity can be tuned to increase the accuracy and reduce the training time of neural networks. Our Preliminary studies have shown that the introduction of diversity in the response of the neurons in a neural network does indeed demonstrate a Stochastic resonance type effect in that accuracy does indeed increase then decrease with increasing diversity while training times do indeed decrease then increase again with increasing diversity. Thus, we propose to develop what we call Diverse Neural Networks (DNNs) which should have wide ranging applications to Artificial Intelligence. Wewill advance neural networks and Artificial Intelligence in a variety of systems and developed methods that internalize the characteristics and embody an understanding of nonlinear, chaotic dynamics and mixtures of chaos and order into the basic operating principles of the neural networks and AIs. We propose to develop foundations and methods for the enhancement, indeed paradigm shifting changes to conventional neural networks and AIs that are both chaos aware (i.e., not blind to chaotic dynamics) as well as a jumping offpoint for the development of chaos-based AI systems ranging from neural networks based upon chaotic universal logic gates (Chaogates) to novel software and hardware systems that understand, exploit and discover nonlinear dynamical systems.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jun 09, 2021
- Source ID
- N000142112354
Entities
People
- William L. Ditto
Organizations
- North Carolina State University
- Office of Naval Research
- United States Navy