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State estimation in water distribution networks (WDN), the problem of estimating all unknown network heads and flows given select measurements, is challenging due to the nonconvexity of hydraulic models and significant uncertainty from…

In this paper, we elaborate over the well-known interpretability issue in echo state networks. The idea is to investigate the dynamics of reservoir neurons with time-series analysis techniques taken from research on complex systems.…

Reliable predictive uncertainty estimation plays an important role in enabling the deployment of neural networks to safety-critical settings. A popular approach for estimating the predictive uncertainty of neural networks is to define a…

In this paper, the problem of proactive caching is studied for cloud radio access networks (CRANs). In the studied model, the baseband units (BBUs) can predict the content request distribution and mobility pattern of each user, determine…

Echo State Networks (ESNs) are a particular type of untrained Recurrent Neural Networks (RNNs) within the Reservoir Computing (RC) framework, popular for their fast and efficient learning. However, traditional ESNs often struggle with…

Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…

In the last decade, a new computational paradigm was introduced in the field of Machine Learning, under the name of Reservoir Computing (RC). RC models are neural networks which a recurrent part (the reservoir) that does not participate in…

This paper examines Echo State Network, a reservoir computer, performance using four different benchmark problems, then proposes heuristics or rules of thumb for configuring the architecture, as well as the selection of parameters and their…

Echo state networks (ESN), a type of reservoir computing (RC) architecture, are efficient and accurate artificial neural systems for time series processing and learning. An ESN consists of a core of recurrent neural networks, called a…

The goal of this paper is to investigate the theoretical properties, the training algorithm, and the predictive control applications of Echo State Networks (ESNs), a particular kind of Recurrent Neural Networks. First, a condition…

In this paper we demonstrate that reservoir computing can be used to learn the dynamics of the shallow-water equations. In particular, while most previous applications of reservoir computing have required training on a particular trajectory…

Making accurate predictions of chaotic time series is a complex challenge. Reservoir computing, a neuromorphic-inspired approach, has emerged as a powerful tool for this task. It exploits the memory and nonlinearity of dynamical systems…

Even though probabilistic treatments of neural networks have a long history, they have not found widespread use in practice. Sampling approaches are often too slow already for simple networks. The size of the inputs and the depth of typical…

We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their…

A reservoir computer is a special type of neural network, where most of the weights are randomly fixed and only a subset are trained. In this thesis we prove results about reservoir computers trained on deterministic dynamical systems, and…

We present a proximal algorithm that performs a variational recursion on the space of joint probability measures to propagate the stochastic uncertainties in power system dynamics over high dimensional state space. The proposed algorithm…

This paper investigates the use of probabilistic neural networks (PNNs) to model aleatoric uncertainty, which refers to the inherent variability in the input-output relationships of a system, often characterized by unequal variance or…

In this technical report we study the problem of propagation of uncertainty (in terms of variances of given uni-variate normal random variables) through typical building blocks of a Convolutional Neural Network (CNN). These include layers…

Bayesian Neural Networks (BNNs) provide a tool to estimate the uncertainty of a neural network by considering a distribution over weights and sampling different models for each input. In this paper, we propose a method for uncertainty…

Recurrent neural networks are machine learning algorithms which are suited well to predict time series. Echo state networks are one specific implementation of such neural networks that can describe the evolution of dynamical systems by…