Related papers: Nonlinear Autoregression with Convergent Dynamics …
In this paper we discuss how the notion of subgeometric ergodicity in Markov chain theory can be exploited to study stationarity and ergodicity of nonlinear time series models. Subgeometric ergodicity means that the transition probability…
Reservoir computing, a machine learning framework used for modeling the brain, can predict temporal data with little observations and minimal computational resources. However, it is difficult to accurately reproduce the long-term target…
The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…
Nonstationary spatial processes can often be represented as stationary processes on a warped spatial domain. Selecting an appropriate spatial warping function for a given application is often difficult and, as a result of this, warping…
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…
Currently, legal requirements demand that insurance companies increase their emphasis on monitoring the risks linked to the underwriting and asset management activities. Regarding underwriting risks, the main uncertainties that insurers…
We consider covariance control problems for nonlinear stochastic systems. Our objective is to find an optimal control strategy to steer the state from an initial distribution to a terminal one with specified mean and covariance. This…
Novel nonlinear damping control is proposed for the second-order systems. The proportional output feedback is combined with the damping term which is quadratic to the output derivative and inverse to the set-point distance. The global…
Neural networks have found extensive application in data-driven control of nonlinear dynamical systems, yet fast online identification and control of unknown dynamics remain central challenges. To meet these challenges, this paper…
In this paper, we design a novel distributed learning algorithm using stochastic compressed communications. In detail, we pursue a modular approach, merging ADMM and a gradient-based approach, benefiting from the robustness of the former…
Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…
We propose a statistical-stochastic surrogate modeling approach to predict the response of the mean and variance statistics under various initial conditions and external forcing perturbations. The proposed modeling framework extends the…
Reservoir Computing (RC) is a powerful computational paradigm that allows high versatility with cheap learning. While other artificial intelligence approaches need exhaustive resources to specify their inner workings, RC is based on a…
We introduce a novel framework of reservoir computing. Cellular automaton is used as the reservoir of dynamical systems. Input is randomly projected onto the initial conditions of automaton cells and nonlinear computation is performed on…
We review attempts that have been made towards understanding the computational properties and mechanisms of input-driven dynamical systems like RNNs, and reservoir computing networks in particular. We provide details on methods that have…
Nonlinear waves have played a historical role in laying the foundations of the science of complexity. Recently, they have also allowed the development of a new reservoir computing paradigm: neuromorphic computing by waves. In these systems,…
Autoregressive models are ubiquitous tools for the analysis of time series in many domains such as computational neuroscience and biomedical engineering. In these domains, data is, for example, collected from measurements of brain activity.…
Quantum computing and neural networks show great promise for the future of information processing. In this paper we study a quantum reservoir computer (QRC), a framework harnessing quantum dynamics and designed for fast and efficient…
Topological textures in magnetic and electric materials are considered to be promising candidates for next-generation information technology and unconventional computing. Here, we discuss how the physical properties of topological nanoscale…
An adiabatic approximation in terms of instantaneous resonances is developed to study the steady-state and time-dependent transport of interacting electrons in biased resonant tunneling heterostructures. The resulting model consists of…