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We present DEF (\textbf{\ul{D}}iffusion-augmented \textbf{\ul{E}}nsemble \textbf{\ul{F}}orecasting), a novel approach for generating initial condition perturbations. Modern approaches to initial condition perturbations are primarily…

Polynomial chaos based methods enable the efficient computation of output variability in the presence of input uncertainty in complex models. Consequently, they have been used extensively for propagating uncertainty through a wide variety…

Physical parameterizations are used as representations of unresolved subgrid processes within weather and global climate models or coarse-scale turbulent models, whose resolutions are too coarse to resolve small-scale processes. These…

Strongly nonlinear flows, which commonly arise in geophysical and engineering turbulence, are characterized by persistent and intermittent energy transfer between various spatial and temporal scales. These systems are difficult to model and…

In autonomous driving, accurate motion prediction is crucial for safe and efficient motion planning. To ensure safety, planners require reliable uncertainty estimates of the predicted behavior of surrounding agents, yet this aspect has…

Ensemble forecasting is a technique devised to palliate sensitivity to initial conditions in nonlinear dynamical systems. The basic idea to avoid this sensitivity is to run the model many times under several slightly-different initial…

The goal of ensemble forecasting is to maximise sharpness subject to reliability. Marginal reliability means that, over all cases, the ensemble is statistically consistent with reality: the ensemble mean is unbiased, the expected ensemble…

We consider a class of uncertain linear time-invariant overparametrized systems affected by bounded disturbances, which are described by a known exosystem with unknown initial conditions. For such systems an exponentially stable extended…

Ensemble data assimilation techniques form an indispensable part of numerical weather prediction. As the ensemble size grows and model resolution increases, the amount of required storage becomes a major issue. Data compression schemes may…

Data-driven reduced order modeling of chaotic dynamics can result in systems that either dissipate or diverge catastrophically. Leveraging non-linear dimensionality reduction of autoencoders and the freedom of non-linear operator inference…

Mesoscale forecasts are now routinely performed as elements of operational forecasts and their outputs do appear convincing. However, despite their realistic appearance at times the comparison to observations is less favorable. At the grid…

Many natural systems exhibit chaotic behaviour such as the weather, hydrology, neuroscience and population dynamics. Although many chaotic systems can be described by relatively simple dynamical equations, characterizing these systems can…

Weather forecasting has seen a shift in methods from numerical simulations to data-driven systems. While initial research in the area focused on deterministic forecasting, recent works have used diffusion models to produce skillful ensemble…

Statistical post-processing techniques are now widely used to correct systematic biases and errors in calibration of ensemble forecasts obtained from multiple runs of numerical weather prediction models. A standard approach is the ensemble…

Probabilistic forecasts in the form of ensemble of scenarios are required for complex decision making processes. Ensemble forecasting systems provide such products but the spatio-temporal structures of the forecast uncertainty is lost when…

Statistical learning algorithms provide a generally-applicable framework to sidestep time-consuming experiments, or accurate physics-based modeling, but they introduce a further source of error on top of the intrinsic limitations of the…

AI weather prediction ensembles with latent noise injection and optimized with the continuous ranked probability score (CRPS) have produced both accurate and well-calibrated predictions with far less computational cost compared with…

Often the underlying system of differential equations driving a stochastic dynamical system is assumed to be known, with inference conditioned on this assumption. We present a Bayesian framework for discovering this system of differential…

Contemporary weather forecasts are typically based on ensemble prediction systems, which consist of multiple runs of numerical weather prediction models that vary with respect to in the initial conditions and/or the the parameterization of…

Accurate forecasting is important for decision-makers. Recently, the Amazon rainforest is reaching record levels of the number of fires, a situation that concerns both climate and public health problems. Obtaining the desired forecasting…