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This review synthesizes recent advancements in understanding tipping points and cascading transitions within the Earth system, framing them through the lens of nonlinear dynamics and complexity science. It outlines the fundamental concepts…
We introduce a geometric method for identifying the coupling direction between two dynamical systems based on a bivariate extension of recurrence network analysis. Global characteristics of the resulting inter-system recurrence networks…
Energy system models underpin decisions by energy system planners and operators. Energy system modelling faces a transformation: accounting for changing meteorological conditions imposed by climate change. To enable that transformation, a…
Environmental science almost invariably proposes problems of extreme complexity, typically characterized by strongly nonlinear evolution dynamics. The systems under investigation have many degrees of freedom - which makes them complicated -…
Causality plays a central role in understanding interactions between variables in complex systems. These systems often exhibit state-dependent causal relationships, where both the strength and direction of causality vary with the value of…
Global climate warming poses a significant challenge to humanity; it is associated with, e.g., rising sea level and declining Arctic sea ice. Increasing extreme events are also considered to be a result of climate…
We describe a simple automated method to extract and quantify transient heterogeneous dynamical changes from large datasets generated in single molecule/particle tracking experiments. Based on wavelet transform, the method transforms raw…
The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a great variety of complex systems has been successfully described as networks whose…
A proper description of ocean-atmosphere interactions is key for a correct understanding of climate evolution. The interplay among the different variables acting over the climate is complex, often leading to correlations across long spatial…
A recent mode coupling theory of higher-order correlation functions is tested on a simple hard-sphere fluid system at intermediate densities. Multi-point and multi-time correlation functions of the densities of conserved variables are…
We propose a data-driven framework to simplify the description of spatiotemporal climate variability into few entities and their causal linkages. Given a high-dimensional climate field, the methodology first reduces its dimensionality into…
Dynamics of complex social systems has often been described in the framework of temporal networks, where links are considered to exist only at the moment of interaction between nodes. Such interaction patterns are not only driven by…
To understand the non-equilibrium relaxation dynamics of a liquid droplet on a switchable substrate the interplay of different length- and time-scales needs to be understood. We present a method to map the microscopic information, resulting…
Geometric deep learning has gained tremendous attention in both academia and industry due to its inherent capability of representing arbitrary structures. Due to exponential increase in interest towards renewable sources of energy,…
This chapter is dedicated to the slow dynamics of the climate system, at time scales of one~thousand to one million years. We focus specifically on the phenomenon of ice ages that has characterised the slow evolution of climate over the…
Accurate and computationally-viable representations of clouds and turbulence are a long-standing challenge for climate model development. Traditional parameterizations that crudely but efficiently approximate these processes are a leading…
In this article, we review the interdisciplinary techniques (borrowed from physics, mathematics, statistics, machine-learning, etc.) and methodological framework that we have used to understand climate systems, which serve as examples of…
We propose a multiscale approach for predicting quantities in dynamical systems which is explicitly structured to extract information in both fine-to-coarse and coarse-to-fine directions. We envision this method being generally applicable…
Understanding the dynamics of climate variables is paramount for numerous sectors, like energy and environmental monitoring. This study focuses on the critical need for a precise mapping of environmental variables for national or regional…
We examine how coupling functions in the theory of dynamical systems provide a quantitative window into climate dynamics. Previously we have shown that a one-dimensional periodic non-autonomous stochastic dynamical system can simulate the…