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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…

Multi-model ensembles provide a pragmatic approach to the representation of model uncertainty in climate prediction. However, such representations are inherently ad hoc, and, as shown, probability distributions of climate variables based on…

In recent years, the development of the Lunar Gateway and Artemis missions has renewed interest in lunar exploration, including both manned and unmanned missions. This interest necessitates accurate initial orbit determination (IOD) and…

We study the evolution of distributions under the action of an ergodic dynamical system, which may be stochastic in nature. By employing tools from Koopman and transfer operator theory one can evolve any initial distribution of the state…

Real-time forecasting from streaming data poses critical challenges: handling non-stationary dynamics, operating under strict computational limits, and adapting rapidly without catastrophic forgetting. However, many existing approaches face…

One essential component of operational space weather forecasting is the prediction of solar flares. With a multitude of flare forecasting methods now available online it is still unclear which of these methods performs best, and none are…

We propose a framework for probabilistic forecasting of dynamical systems based on generative modeling. Given observations of the system state over time, we formulate the forecasting problem as sampling from the conditional distribution of…

The global behavior of dynamical systems can be studied by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with the system. Two important operators which are frequently used to gain insight into the…

Recurrent neural networks are widely used on time series data, yet such models often ignore the underlying physical structures in such sequences. A new class of physics-based methods related to Koopman theory has been introduced, offering…

Reliable forecasts of quasi-stationary, recurrent, and persistent large-scale atmospheric circulation patterns (weather regimes) are crucial for various socio-economic sectors. Despite steady progress, probabilistic weather regime…

The operational reliability of a high performance marine vessel depends critically on the health of its marine propulsion systems, which are increasingly subjected to diverse operational loads and environmental stressors. This paper…

A hybrid data assimilation algorithm is developed for complex dynamical systems with partial observations. The method starts with applying a spectral decomposition to the entire spatiotemporal fields, followed by creating a machine learning…

The Koopman operator provides a principled framework for analyzing nonlinear dynamical systems through linear operator theory. Recent advances in dynamic mode decomposition (DMD) have shown that trajectory data can be used to identify…

The analysis of nonlinear dynamical systems based on the Koopman operator is attracting attention in various applications. Dynamic mode decomposition (DMD) is a data-driven algorithm for Koopman spectral analysis, and several variants with…

Nowadays, weather prediction is based on numerical weather prediction (NWP) models to produce an ensemble of forecasts. Despite of large improvements over the last few decades, they still tend to exhibit systematic bias and dispersion…

Accurate time series forecasting is critical for a wide range of problems with temporal data. Ensemble modeling is a well-established technique for leveraging multiple predictive models to increase accuracy and robustness, as the…

A new efficient ensemble prediction strategy is developed for a general turbulent model framework with emphasis on the nonlinear interactions between large and small scale variables. The high computational cost in running large ensemble…

There is growing interest in data-driven weather prediction (DDWP), for example using convolutional neural networks such as U-NETs that are trained on data from models or reanalysis. Here, we propose 3 components to integrate with commonly…

We present Stochastic Dynamic Mode Decomposition (SDMD), a novel data-driven framework for approximating the Koopman semigroup in stochastic dynamical systems. Unlike existing methods, SDMD explicitly incorporates sampling time into its…

In this paper, we leverage Koopman mode decomposition to analyze the nonlinear and high-dimensional climate systems acting on the observed data space. The dynamics of atmospheric systems are assumed to be equation-free, with the linear…