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Equations of State model relations between thermodynamic variables and are ubiquitous in scientific modelling, appearing in modern day applications ranging from Astrophysics to Climate Science. The three desired properties of a general…

Early warning signals have been proposed to forecast the possibility of a critical transition, such as the eutrophication of a lake, the collapse of a coral reef, or the end of a glacial period. Because such transitions often unfold on…

Complex systems can undergo critical transitions, where slowly changing environmental conditions trigger a sudden shift to a new, potentially catastrophic state. Early warning signals for these events are crucial for decision-making in…

Modern weather and climate models share a common heritage, and often even components, however they are used in different ways to answer fundamentally different questions. As such, attempts to emulate them using machine learning should…

The representation of nonlinear sub-grid processes, especially clouds, has been a major source of uncertainty in climate models for decades. Cloud-resolving models better represent many of these processes and can now be run globally but…

Accurate weather and climate modeling is critical for both scientific advancement and safeguarding communities against environmental risks. Traditional approaches rely heavily on Numerical Weather Prediction (NWP) models, which simulate…

Wireless sensor networks monitor dynamic environments that change rapidly over time. This dynamic behavior is either caused by external factors or initiated by the system designers themselves. To adapt to such conditions, sensor networks…

Despite the importance of quantifying how the spatial patterns of extreme precipitation will change with warming, we lack tools to objectively analyze the storm-scale outputs of modern climate models. To address this gap, we develop an…

Model studies indicate that many climate subsystems, especially ecosystems, may be vulnerable to 'tipping': a 'catastrophic process' in which a system, driven by gradually changing external factors, abruptly transitions (or 'collapses')…

Deep structured models are widely used for tasks like semantic segmentation, where explicit correlations between variables provide important prior information which generally helps to reduce the data needs of deep nets. However, current…

Recent advances in data-generating techniques led to an explosive growth of geo-spatiotemporal data. In domains such as hydrology, ecology, and transportation, interpreting the complex underlying patterns of spatiotemporal interactions with…

The phenomenon of critical slowing down (CSD) has played a key role in the search for reliable precursors of catastrophic regime shifts. This is caused by its presence in a generic class of bifurcating dynamical systems. Simple time-series…

Predicting the future behaviour of complex systems exhibiting critical-like dynamics is often considered to be an intrinsically hard task. Here, we study the predictability of the depinning dynamics of elastic interfaces in random media…

Transitions between distinct dynamical regimes are ubiquitous in nonequilibrium systems. As a prototypical example, deposition growth is often accompanied by irreversible morphological instabilities. Forecasting such transitions from…

Microclimate models are essential for linking climate to ecological processes, yet most physically based frameworks estimate temperature independently for each spatial unit and rely on simplified representations of lateral heat exchange. As…

We present an analysis of neural network-based machine learning schemes for phases and phase transitions in theoretical condensed matter research, focusing on neural networks with a single hidden layer. Such shallow neural networks were…

This study constructs an integrated early warning system (EWS) that identifies and predicts stock market turbulence. Based on switching ARCH (SWARCH) filtering probabilities of the high volatility regime, the proposed EWS first classifies…

Critical transitions and tipping phenomena between two meta-stable states in stochastic dynamical systems are a significant scientific issue. In this work, we expand the methodology of identifying the most probable transition pathway…

State-space models are dynamical systems defined by a latent and an observed process. In ecology, stochastic state-space models in discrete time are most often used to describe the imperfectly observed dynamics of population sizes or animal…

Ecological systems often exhibit complex nonlinear dynamics like oscillations, chaos, and regime shifts. Universal dynamic equations have shown promise in modeling complex dynamics by combining known functional forms with neural networks…