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This work presents an autoregressive generative diffusion model (DiffObs) to predict the global evolution of daily precipitation, trained on a satellite observational product, and assessed with domain-specific diagnostics. The model is…

Subseasonal-to-seasonal (S2S) forecasting, which predicts climate conditions from several weeks to months in advance, represents a critical frontier for agricultural planning, energy management, and disaster preparedness. However, it…

We introduce an interpretable-by-design method, optimized model-analog, that integrates deep learning with model-analog forecasting which generates forecasts from similar initial climate states in a repository of model simulations. This…

Data assimilation techniques, such as ensemble Kalman filtering, have been shown to be a highly effective and efficient way to combine noisy data with a mathematical model to track and forecast dynamical systems. However, when dealing with…

We establish the convergence of a class of numerical algorithms, known as Dynamic Mode Decomposition (DMD), for computation of the eigenvalues and eigenfunctions of the infinite-dimensional Koopman operator. The algorithms act on data…

The accurate modeling of dynamics in interactive environments is critical for successful long-range prediction. Such a capability could advance Reinforcement Learning (RL) and Planning algorithms, but achieving it is challenging.…

Inflow forecasts play an essential role in the management of hydropower reservoirs. Forecasts help operators schedule power generation in advance to maximise economic value, mitigate downstream flood risk, and meet environmental…

Weather forecasting presents several challenges, including the chaotic nature of the atmosphere and the high computational demands of numerical weather prediction models. To achieve the most accurate predictions, the ideal scenario involves…

Ensemble forecasting of nonlinear systems involves the use of a model to run forward a discrete ensemble (or set) of initial states. Data assimilation techniques tend to focus on estimating the true state of the system, even though model…

We propose a novel framework for safe navigation in dynamic environments by integrating Koopman operator theory with conformal prediction. Our approach leverages data-driven Koopman approximation to learn nonlinear dynamics and employs…

In this paper, a data-driven nonparametric approach is presented for forecasting the probability density evolution of stochastic dynamical systems. The method is based on stochastic Koopman operator and extended dynamic mode decomposition…

It has become common to perform kinetic analysis using approximate Koopman operators that transforms high-dimensional time series of observables into ranked dynamical modes. Key to a practical success of the approach is the identification…

Accurate weather forecasting is essential for socioeconomic activities. While data-driven forecasting demonstrates superior predictive capabilities over traditional Numerical Weather Prediction (NWP) with reduced computational demands, its…

Data assimilation provides algorithms for widespread applications in various fields. It is of practical use to deal with a large amount of information in the complex system that is hard to estimate. Weather forecasting is one of the…

Extended Dynamic Mode Decomposition (eDMD) is a powerful tool to generate data-driven surrogate models for the prediction and control of nonlinear dynamical systems in the Koopman framework. In eDMD a compression of the lifted system…

Statistical post-processing of dynamical forecast ensembles is an essential component of weather forecasting. In this article, we present a post-processing method that generates full predictive probability distributions for precipitation…

Probabilistic weather forecasts from ensemble systems require statistical postprocessing to yield calibrated and sharp predictive distributions. This paper presents an area-covering postprocessing method for ensemble precipitation…

Quantifying forecast uncertainty is a key aspect of state-of-the-art numerical weather prediction and data assimilation systems. Ensemble-based data assimilation systems incorporate state-dependent uncertainty quantification based on…

Time series foundation models (TSFMs) such as Lag-Llama, TimeGPT, Chronos, MOMENT, UniTS, and TimesFM have shown strong generalization and zero-shot capabilities for time series forecasting, anomaly detection, classification, and…

Statistical postprocessing is routinely applied to correct systematic errors of numerical weather prediction models (NWP) and to automatically produce calibrated local forecasts for end-users. Postprocessing is particularly relevant in…