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Spectral decomposition of dynamical systems is a popular methodology to investigate the fundamental qualitative and quantitative properties of these systems and their solutions. In this chapter, we consider a class of nonlinear cooperative…
Real-world time series are characterized by intrinsic non-stationarity that poses a principal challenge for deep forecasting models. While previous models suffer from complicated series variations induced by changing temporal distribution,…
Existing methods for diagnosing predictability in climate indices often make a number of unjustified assumptions about the climate system that can lead to misleading conclusions. We present a flexible family of state-space models capable of…
Projecting climate change is a generalization problem: we extrapolate the recent past using physical models across past, present, and future climates. Current climate models require representations of processes that occur at scales smaller…
In this work, we propose to apply the recently developed Koopman operator techniques to explore the global phase space of a nonlinear system from time-series data. In particular, we address the problem of identifying various invariant…
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics like work, heat and entropy production to the level of individual trajectories of well-defined…
We assess empirical models in climate econometrics using modern statistical learning techniques. Existing approaches are prone to outliers, ignore sample dependencies, and lack principled model selection. To address these issues, we…
The Koopman operator induced by a dynamical system is inherently linear and provides an alternate method of studying many properties of the system, including attractor reconstruction and forecasting. Koopman eigenfunctions represent the…
The Koopman and Perron Frobenius transport operators are fundamentally changing how we approach dynamical systems, providing linear representations for even strongly nonlinear dynamics. Although there is tremendous potential benefit of such…
Accurately predicting sea-surface temperature weeks to months into the future is an important step toward long term weather forecasting. Standard atmosphere-ocean coupled numerical models provide accurate sea-surface forecasts on the scale…
The climate system is a complex, chaotic system with many degrees of freedom and variability on a vast range of temporal and spatial scales. Attaining a deeper level of understanding of its dynamical processes is a scientific challenge of…
Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems. However, existing DMD theory deals primarily with sequential time…
The sine-Gordon model appears as the low-energy effective field theory of various one-dimensional gapped quantum systems. Here we investigate the dynamics of generic, non-integrable systems belonging to the sine-Gordon family at finite…
Formation control of multi-agent systems has been a prominent research topic, spanning both theoretical and practical domains over the past two decades. Our study delves into the leader-follower framework, addressing two critical,…
A turbocharger plays an essential part in reducing emissions and increasing the fuel efficiency of road vehicles. The pulsating flow of exhaust gases, along with high heat exchange from the turbocharger casing, makes developing…
A single-column model is used to investigate regime transitions within the stable atmospheric boundary layer, focusing on the role of small-scale fluctuations in wind and temperature dynamics and of turbulence intermittency as triggers for…
It is hard to identify nonlinear biological models strictly from data, with results that are often sensitive to experimental conditions. Automated experimental workflows and liquid handling enables unprecedented throughput, as well as the…
Employing a recently developed approach to dynamically emergent quantum thermodynamics, we revisit the thermodynamic behavior of the quantum Otto cycle with a focus on memory effects and strong system-bath couplings. Our investigation is…
Periodically driven quantum systems can be used to realize quantum pumps, ratchets, artificial gauge fields and novel topological states of matter. Starting from the Keldysh approach, we develop a formalism, the Floquet-Boltzmann equation,…
This paper studies a regression model with functional dependent and explanatory variables, both of which exhibit nonstationary dynamics. The model assumes that the nonstationary stochastic trends of the dependent variable are explained by…