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Time series forecasting (TSF) is critical across domains such as finance, meteorology, and energy. While extending the lookback window theoretically provides richer historical context, in practice, it often introduces irrelevant noise and…
The configuration of physical parameterization schemes in Numerical Weather Prediction (NWP) models plays a critical role in determining the accuracy of the forecast. However, existing parameter calibration methods typically treat each…
Ensembles of forecasts are obtained from multiple runs of numerical weather forecasting models with different initial conditions and typically employed to account for forecast uncertainties. However, biases and dispersion errors often occur…
El Ni\~no Southern Oscillation (ENSO) diversity is characterized based on the longitudinal location of maximum sea surface temperature anomalies (SSTA) and amplitude in the tropical Pacific, as Central Pacific (CP) events are typically…
Data assimilation plays a key role in large-scale atmospheric weather forecasting, where the state of the physical system is estimated from model outputs and observations, and is then used as initial condition to produce accurate future…
The path toward realizing the potential of seasonal forecasting and its socioeconomic benefits depends heavily on improving general circulation model based dynamical forecasting systems. To improve dynamical seasonal forecast, it is crucial…
We propose a nonparametric approach for probabilistic prediction of the AL index trained with AL and solar wind ($v B_z$) data. Our framework relies on the diffusion forecasting technique, which views AL and $ v B_z $ data as observables of…
The El Nino southern oscillation (ENSO) behavior can be effectively modeled as a response to a 2nd-order Mathieu/Hill differential equation with periodic coefficients describing sloshing of a volume of water. The forcing of the equation…
We study the forced response of the teleconnection between the El Nino-Southern Oscillation (ENSO) and global precipitation in general and the Indian summer monsoon (IM) in particular in the Max Planck Institute Grand Ensemble. The forced…
Accurate long-term predictions are the foundations for many machine learning applications and decision-making processes. However, building accurate long-term prediction models remains challenging due to the limitations of existing temporal…
Neural operators extend data-driven models to map between infinite-dimensional functional spaces. These models have successfully solved continuous dynamical systems represented by differential equations, viz weather forecasting, fluid flow,…
Effective resource management and environmental planning in regions with high climatic variability, such as Chile, demand advanced predictive tools. This study addresses this challenge by employing an innovative and computationally…
The lacking of analytic solutions of diverse partial differential equations (PDEs) gives birth to a series of computational techniques for numerical solutions. Although numerous latest advances are accomplished in developing neural…
This is the last part of four series papers, aiming at stabilization for signal-input-signaloutput (SISO) linear finite-dimensional systems corrupted by general input disturbances. A new observer, referred to as Extended Dynamics Observer…
El Ni\~no Southern Oscillation (ENSO) is the Earth's strongest source of interannual climate variability. Although its center of action is in the tropical Pacific, it has significant influences on the climate at the planetary scale. ENSO is…
We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their…
The problem of prediction of a given time series is examined on the basis of recent nonlinear dynamics theories. Particular attention is devoted to forecast the amplitude and phase of one of the most common solar indicator activity, the…
Accurate modeling and prediction of complex physical systems often rely on data assimilation techniques to correct errors inherent in model simulations. Traditional methods like the Ensemble Kalman Filter (EnKF) and its variants as well as…
The ensemble Kalman filter (EnKF) is a method for combining a dynamical model with data in a sequential fashion. Despite its widespread use, there has been little analysis of its theoretical properties. Many of the algorithmic innovations…
Atmospheric wavefront prediction based on previous wavefront sensor measurements can greatly enhance the performance of adaptive optics systems. We propose an optimal linear approach based on the Empirical Orthogonal Functions (EOF)…