Related papers: Learning Chaotic Dynamics with Neuromorphic Networ…

Neuromorphic computing and spiking neural networks (SNN) mimic the behavior of biological systems and have drawn interest for their potential to perform cognitive tasks with high energy efficiency. However, some factors such as temporal…

Modeling of conservative systems with neural networks is an area of active research. A popular approach is to use Hamiltonian neural networks (HNNs) which rely on the assumptions that a conservative system is described with Hamilton's…

We present a structured neural network architecture that is inspired by linear time-varying dynamical systems. The network is designed to mimic the properties of linear dynamical systems which makes analysis and control simple. The…

Studies regarding knowledge organization and acquisition are of great importance to understand areas related to science and technology. A common way to model the relationship between different concepts is through complex networks. In such…

We study the learning ability of linear recurrent neural networks with Gradient Descent. We prove the first theoretical guarantee on linear RNNs to learn any stable linear dynamic system using any a large type of loss functions. For an…

Modeling dynamical systems plays a crucial role in capturing and understanding complex physical phenomena. When physical models are not sufficiently accurate or hardly describable by analytical formulas, one can use generic function…

Identifying a linear system model from data has wide applications in control theory. The existing work on finite sample analysis for linear system identification typically uses data from a single system trajectory under i.i.d random inputs,…

Improving the interpretability of deep neural networks has recently gained increased attention, especially when the power of deep learning is leveraged to solve problems in physics. Interpretability helps us understand a model's ability to…

We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…

We develop a learning-based algorithm for the distributed formation control of networked multi-agent systems governed by unknown, nonlinear dynamics. Most existing algorithms either assume certain parametric forms for the unknown dynamic…

Brain-inspired learning in physical hardware has enormous potential to learn fast at minimal energy expenditure. One of the characteristics of biological learning systems is their ability to learn in the presence of various noise sources.…

In this paper, we introduce a novel architecture to connecting adaptive learning and neural networks into an arbitrary machine's control system paradigm. Two consecutive Recurrent Neural Networks (RNNs) are used together to accurately model…

Deep neural networks give us a powerful method to model the training dataset's relationship between input and output. We can regard that as a complex adaptive system consisting of many artificial neurons that work as an adaptive memory as a…

In this paper we consider networks of dynamical systems that evolve in synchrony and investigate how dynamical information from the synchronization dynamics can be effectively used to learn the network topology, i.e., identify the time…

This paper focuses on analysis and design of time-varying complex networks having fractional order dynamics. These systems are key in modeling the complex dynamical processes arising in several natural and man made systems. Notably,…

We study the dynamics of on-line learning in large perceptrons, for the case of training sets with a structural bias of the input vectors, by deriving exact and closed macroscopic dynamical laws using non-equilibrium statistical mechanical…

We investigate the use of discrete and continuous versions of physics-informed neural network methods for learning unknown dynamics or constitutive relations of a dynamical system. For the case of unknown dynamics, we represent all the…

The purpose of this paper is to infer a global (collective) model of time-varying responses of a set of nodes as a dynamic graph, where the individual time series are respectively observed at each of the nodes. The motivation of this work…

Deep Learning has received increased attention due to its unbeatable success in many fields, such as computer vision, natural language processing, recommendation systems, and most recently in simulating multiphysics problems and predicting…

Artificial neural networks which are inspired from the learning mechanism of brain have achieved great successes in many problems, especially those with deep layers. In this paper, we propose a nucleus neural network (NNN) and corresponding…