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Different methods are used to determine the scaling exponents associated with a time series describing a complex dynamical process, such as those observed in geophysical systems. Many of these methods are based on the numerical evaluation…

Turbulence is an out-of-equilibrium flow state that is characterised by nonzero net fluxes of kinetic energy between different scales of the flow. These fluxes play a crucial role in the formation of characteristic flow structures in many…

Estimating spatially distributed information through the interpolation of scattered observation datasets often overlooks the critical role of domain knowledge in understanding spatial dependencies. Additionally, the features of these data…

Multistability is a phenomenon prevalent in many natural systems. In climate, for example, it allows the possibility of irreversible consequences on planetary scale as a result of climate change. Indeed, a climate ``tipping element'' is a…

Understanding solar flares is critical for predicting space weather, as their activity shapes how the Sun influences Earth and its environment. The development of reliable forecasting methodologies of these events depends on robust flare…

Accurate prediction of human or vehicle trajectories with good diversity that captures their stochastic nature is an essential task for many applications. However, many trajectory prediction models produce unreasonable trajectory samples…

Time series forecasting, which aims to predict future values based on historical data, has garnered significant attention due to its broad range of applications. However, real-world time series often exhibit complex non-uniform distribution…

Climate emulation is an out-of-distribution (OOD) projection task. This is precisely the challenge where modern Machine Learning (ML) methods are most prone to failure. Consequently, while current ML emulators trained on present climate…

We analyze ecological systems that are influenced by random environmental fluctuations. We first provide general conditions which ensure that the species coexist and the system converges to a unique invariant probability measure (stationary…

Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were…

The natural cycles of the surface-to-atmosphere fluxes of carbon dioxide (CO$_2$) and other important greenhouse gases are changing in response to human influences. These changes need to be quantified to understand climate change and its…

Models of the spatial distribution of animals provide useful tools to help ecologists quantify species-environment relationships, and they are increasingly being used to help determine the impacts of climate and habitat changes on species.…

Current endeavours in exoplanet characterisation rely on atmospheric retrieval to quantify crucial physical properties of remote exoplanets from observations. However, the scalability and efficiency of the technique are under strain with…

Scene flow estimation is the task of describing 3D motion between temporally successive observations. This thesis aims to build the foundation for building scene flow estimators with two important properties: they are scalable, i.e. they…

Reusing pre-collected data from different domains is an appealing solution for decision-making tasks, especially when data in the target domain are limited. Existing cross-domain policy transfer methods mostly aim at learning domain…

Partially Supervised Multi-Task Learning (PS-MTL) aims to leverage knowledge across tasks when annotations are incomplete. Existing approaches, however, have largely focused on the simpler setting of homogeneous, dense prediction tasks,…

Tropical cyclone (TC) forecasting is critical for disaster warning and emergency response. Deep learning methods address computational challenges but often neglect physical relationships between TC attributes, resulting in predictions…

While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting,…

Terrestrial carbon fluxes provide vital information about our biosphere's health and its capacity to absorb anthropogenic CO$_2$ emissions. The importance of predicting carbon fluxes has led to the emerging field of data-driven carbon flux…

Cross-domain time series imputation is an underexplored data-centric research task that presents significant challenges, particularly when the target domain suffers from high missing rates and domain shifts in temporal dynamics. Existing…