Related papers: Predictability in Nonlinear Dynamical Systems with…

Can we conclude the stability of an unknown dynamical system from the knowledge of a finite number of snapshots of trajectories? We tackle this black-box problem for switched linear systems. We show that, for any given random set of…

We present an optimization process to estimate parameters in systems of ordinary differential equations from chaotic time series. The optimization technique is based on a variational approach, and numerical studies on noisy time series…

This paper deals with the noise identification of a linear time-varying stochastic dynamic system described by the state-space model. In particular, the stress is laid on the design of the correlation measurement difference method for…

This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…

In this paper, we study networks of positive linear systems subject to time-invariant and random uncertainties. We present linear matrix inequalities for checking the stability of the whole network around the origin with prescribed…

Models are often given in terms of differential equations to represent physical systems. In the presence of uncertainty, accurate prediction of the behavior of these systems using the models requires understanding the effect of uncertainty…

Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent…

Future energy systems are subject to various uncertain influences. As resilient systems they should maintain a constantly high operational performance whatever happens. We explore different levels and time scales of decision making in…

Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…

Learning and forecasting stochastic time series is essential in various scientific fields. However, despite the proposals of nonlinear filters and deep-learning methods, it remains challenging to capture nonlinear dynamics from a few noisy…

A parameter estimation problem for a class of semilinear stochastic evolution equations is considered. Conditions for consistency and asymptotic normality are given in terms of growth and continuity properties of the nonlinear part.…

This brief introduction to Model Predictive Control specifically addresses stochastic Model Predictive Control, where probabilistic constraints are considered. A simple linear system subject to uncertainty serves as an example. The Matlab…

The inability of artificial neural networks to assess the uncertainty of their predictions is an impediment to their widespread use. We distinguish two types of learnable uncertainty: model uncertainty due to a lack of training data and…

Predicting the response of nonlinear dynamical systems subject to random, broadband excitation is important across a range of scientific disciplines, such as structural dynamics and neuroscience. Building data-driven models requires…

Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One…

Complex numerical weather prediction models incorporate a variety of physical processes, each described by multiple alternative physical schemes with specific parameters. The selection of the physical schemes and the choice of the…

A comprehensive uncertainty estimation is vital for the precision program of the LHC. While experimental uncertainties are often described by stochastic processes and well-defined nuisance parameters, theoretical uncertainties lack such a…

The vast majority of stochastic simulation models are imperfect in that they fail to exactly emulate real system dynamics. The inexactness of the simulation model, or model discrepancy, can impact the predictive accuracy and usefulness of…

We present a framework for learning of modeling uncertainties in Linear Time Invariant (LTI) systems. We propose a methodology to extend the dynamics of an LTI (without uncertainty) with an uncertainty model, based on measured data, to…

For applications of machine learning in critical decisions, explainability is a primary concern, and often a regulatory requirement. Local linear methods for generating explanations, such as LIME and SHAP, have been criticized for being…