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Distinguishability and, by extension, observability are key properties of dynamical systems. Establishing these properties is challenging, especially when no analytical model is available and they are to be inferred directly from…
Physically motivated stochastic dynamics are often used to sample from high-dimensional distributions. However such dynamics often get stuck in specific regions of their state space and mix very slowly to the desired stationary state. This…
Predictive skill of complex models is often not uniform in model-state space; in weather forecasting models, for example, the skill of the model can be greater in populated regions of interest than in "remote" regions of the globe. Given a…
Global climate models aim to reproduce physical processes on a global scale and predict quantities such as temperature given some forcing inputs. We consider climate ensembles made of collections of such runs with different initial…
Empirical modelling often aims for the simplest model consistent with the data. A new technique is presented which quantifies the consistency of the model dynamics as a function of location in state space. As is well-known, traditional…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
Ensemble prediction systems are an invaluable tool for weather forecasting. Practically, ensemble predictions are obtained by running several perturbations of the deterministic control forecast. However, ensemble prediction is associated…
The problem of statistical inference for open chaotic systems measured with error is complicated by the interaction of the uncertainty introduced by chaos, and the various sources of random or external variation. Here a method of…
Making the most of multispectral image time-series is a promising but still relatively under-explored research direction because of the complexity of jointly analyzing spatial, spectral and temporal information. Capturing and characterizing…
Utilizing the information in observations of a complex system to make accurate predictions through a quantitative model when observations are completed at time $T$, requires an accurate estimate of the full state of the model at time $T$.…
We study a system whose dynamics are governed by predictions of its future states. A general formalism and concrete examples are presented. We find that the dynamical characteristics depend on how to shape the predictions as well as on how…
To analyze high-dimensional systems, many fields in science and engineering rely on high-level descriptions, sometimes called "macrostates," "coarse-grainings," or "effective theories". Examples of such descriptions include the…
Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…
Statistical physics and dynamical systems theory are key tools to study high-impact geophysical events such as temperature extremes, cyclones, thunderstorms, geomagnetic storms and many more. Despite the intrinsic differences between these…
With the press of global climate change, extreme weather and sudden weather changes are becoming increasingly common. To maintain a comfortable indoor environment and minimize the contribution of the building to climate change as much as…
Ensemble weather predictions require statistical post-processing of systematic errors to obtain reliable and accurate probabilistic forecasts. Traditionally, this is accomplished with distributional regression models in which the parameters…
Weather forecasts sit upstream of high-stakes decisions in domains such as grid operations, aviation, agriculture, and emergency response. Yet forecast users often face a difficult trade-off. Many decision-relevant targets are functionals…
Atmospheric modeling has recently experienced a surge with the advent of deep learning. Most of these models, however, predict concentrations of pollutants following a data-driven approach in which the physical laws that govern their…
A promising approach to improve climate-model simulations is to replace traditional subgrid parameterizations based on simplified physical models by machine learning algorithms that are data-driven. However, neural networks (NNs) often lead…
Bayesian analysis of state-space models includes computing the posterior distribution of the system's parameters as well as filtering, smoothing, and predicting the system's latent states. When the latent states wander around $\mathbb{R}^n$…