Related papers: Analog Forecasting with Dynamics-Adapted Kernels

Numerous studies have focused on learning and understanding the dynamics of physical systems from video data, such as spatial intelligence. Artificial intelligence requires quantitative assessments of the uncertainty of the model to ensure…

We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning. Our approach pairs a novel automatically constructed analytic expansion of the underlying kernel function…

Weather and climate forecasts are inherently uncertain due to chaotic dynamics, imperfect initial conditions, and incomplete representation of the underlying physical processes. Operational ensemble forecasts aim to represent these…

Multi-year-to-decadal climate prediction is a key tool in understanding the range of potential regional and global climate futures. Here, we present a framework that combines machine learning and analog forecasting for predictions on these…

This paper serves as a bridge between quantum computing and analogical modeling (a general theory for predicting categories of behavior in varying contexts). Since its formulation in the early 1980s, analogical modeling has been…

Representing and quantifying uncertainty in physical parameterisations is a central challenge in weather and climate modelling, and approaches are often developed separately for different timescales. Here, we introduce a unified framework…

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…

Ensemble forecasting is, so far, the most successful approach to produce relevant forecasts with an estimation of their uncertainty. The main limitations of ensemble forecasting are the high computational cost and the difficulty to capture…

Traditional linear methods for forecasting multivariate time series are not able to satisfactorily model the non-linear dependencies that may exist in non-Gaussian series. We build on the theory of learning vector-valued functions in the…

Scientific analysis often relies on the ability to make accurate predictions of a system's dynamics. Mechanistic models, parameterized by a number of unknown parameters, are often used for this purpose. Accurate estimation of the model…

Machine learning models can represent climate processes that are nonlocal in horizontal space, height, and time, often by combining information across these dimensions in highly nonlinear ways. While this can improve predictive skill, it…

Since their emergence in the 1990's, the support vector machine and the AdaBoost algorithm have spawned a wave of research in statistical machine learning. Much of this new research falls into one of two broad categories: kernel methods and…

Many dynamical systems are difficult or impossible to model using high fidelity physics based models. Consequently, researchers are relying more on data driven models to make predictions and forecasts. Based on limited training data,…

Dynamics of complex systems is studied by first considering a chaotic time series generated by Lorenz equations and adding noise to it. The trend (smooth behavior) is separated from fluctuations at different scales using wavelet analysis…

Probabilistic forecasting provides a principled framework for uncertainty quantification in dynamical systems by representing predictions as probability distributions rather than deterministic trajectories. However, existing forecasting…

This work presents a hybrid modeling approach to data-driven learning and representation of unknown physical processes and closure parameterizations. These hybrid models are suitable for situations where the mechanistic description of…

Among the most relevant processes in the Earth system for human habitability are quasi-periodic, ocean-driven multi-year events whose dynamics are currently incompletely characterized by physical models, and hence poorly predictable. This…

We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data is in the form of noisy partial measurements of the past and present state of the dynamical system. Recently there have been several…

Systems exhibiting nonlinear dynamics, including but not limited to chaos, are ubiquitous across Earth Sciences such as Meteorology, Hydrology, Climate and Ecology, as well as Biology such as neural and cardiac processes. However, System…

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…