Related papers: Limits to extreme event forecasting in chaotic sys…
Climate change is increasing the occurrence of extreme precipitation events, threatening infrastructure, agriculture, and public safety. Ensemble prediction systems provide probabilistic forecasts but exhibit biases and difficulties in…
Adaptive dynamical systems arise in a multitude of contexts, e.g., optimization, control, communications, signal processing, and machine learning. A precise characterization of their fundamental limitations is therefore of paramount…
Complex Event Recognition applications exhibit various types of uncertainty, ranging from incomplete and erroneous data streams to imperfect complex event patterns. We review Complex Event Recognition techniques that handle, to some extent,…
In this manuscript we continue the thread of [M. Chertkov, F. Pan, M. Stepanov, Predicting Failures in Power Grids: The Case of Static Overloads, IEEE Smart Grid 2011] and suggest a new algorithm discovering most probable extreme stochastic…
The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…
The remarkable flexibility and adaptability of both deep learning models and ensemble methods have led to the proliferation for their application in understanding many physical phenomena. Traditionally, these two techniques have largely…
In this paper, we derive generic bounds on the maximum deviations in prediction errors for sequential prediction via an information-theoretic approach. The fundamental bounds are shown to depend only on the conditional entropy of the data…
Quantifying and predicting rare and extreme events persists as a crucial yet challenging task in understanding complex dynamical systems. Many practical challenges arise from the infrequency and severity of these events, including the…
Although the fundamental probabilistic theory of extremes has been well developed, there are many practical considerations that must be addressed in application. The contribution of this thesis is four-fold. The first concerns the choice of…
Complexity is an important metric for appropriate characterization of different classes of irregular signals, observed in the laboratory or in nature. The literature is already rich in the description of such measures using a variety of…
Traditionally, Probability theory was dealing with limit theorems where 'limit" means that time tends to infinity. Questions about finite time dynamics (evolution) were always considered as, although important for practical applications,…
Machine learning classification methods usually assume that all possible classes are sufficiently present within the training set. Due to their inherent rarities, extreme events are always under-represented and classifiers tailored for…
This work studies the effectiveness of several machine learning techniques for predicting extreme events occurring in the flow around an airfoil at low Reynolds. For certain Reynolds numbers the aerodynamic forces exhibit intermittent…
Dynamical systems with high intrinsic dimensionality are often characterized by extreme events having the form of rare transitions several standard deviations away from the mean. For such systems, order-reduction methods through projection…
An information-theoretic framework is developed to assess the predictability of ENSO complexity, which is a central problem in contemporary meteorology with large societal impacts. The information theory advances a unique way to quantify…
When an expert operates a perilous dynamic system, ideal constraint information is tacitly contained in their demonstrated trajectories and controls. The likelihood of these demonstrations can be computed, given the system dynamics and task…
Extreme weather is one of the main mechanisms through which climate change will directly impact human society. Coping with such change as a global community requires markedly improved understanding of how global warming drives extreme…
Suppose we are given a time series or a signal $x(t)$ for $0\leq t\leq T$. We consider the problem of predicting the signal in the interval $T<t\leq T+t_{f}$ from a knowledge of its history and nothing more. We ask the following question:…
Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize…
In this paper, we consider contention resolution algorithms that are augmented with predictions about the network. We begin by studying the natural setup in which the algorithm is provided a distribution defined over the possible network…