Related papers: Time Series Forecasting: A Nonlinear Dynamics Appr…

In the era of increasingly complex AI models for time series forecasting, progress is often measured by marginal improvements on benchmark leaderboards. However, this approach suffers from a fundamental flaw: standard evaluation metrics…

We examine contributions of second order physical processes to results of stellar evolution calculations amenable to direct observational testing. In the first paper in the series (Young et al. 2001) we established baseline results using…

Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict…

The application of linear kinetic treatments to plasma waves, damping, and instability requires favorable inequalities between the associated linear timescales and timescales for nonlinear (e.g., turbulence) evolution. In the solar wind…

Spatiotemporal forecasting is critical for real-world applications like traffic management, yet capturing reliable interactions remains challenging under noisy and non-stationary conditions. Existing methods primarily rely on historical…

Time series forecasting has gained lots of attention recently; this is because many real-world phenomena can be modeled as time series. The massive volume of data and recent advancements in the processing power of the computers enable…

We apply a nonlinear mean-field dynamo model which includes a budget equation for the dynamics of Wolf numbers to predict solar activity. This dynamo model takes into account the algebraic and dynamic nonlinearities of the alpha effect,…

Physical models aimed to reproduce basic features of the solar sunspot cycle are typically based on the solar dynamo mechanism. Usually qualitative arguments are used to define parameters of the model, among which a challenging component is…

We calculate accurate solar models and report the detailed time dependences of important solar quantities. We use helioseismology to constrain the luminosity evolution of the sun and report the discovery of semi-convection in evolved solar…

Using solar power in the process industry can reduce greenhouse gas emissions and make the production process more sustainable. However, the intermittent nature of solar power renders its usage challenging. Building a model to predict…

We consider multi-task regression models where the observations are assumed to be a linear combination of several latent node functions and weight functions, which are both drawn from Gaussian process priors. Driven by the problem of…

We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system…

The sunspot solar cycle has been usually explained as the result of a dynamo process operating in the sun. This is a classical problem in Astrophysics that until the present is not fully solved. Here we discuss current problems and…

Time series prediction typically consists of a data reconstruction phase where the time series is broken into overlapping windows known as the timespan. The size of the timespan can be seen as a way of determining the extent of past…

This study explores the behavior of machine learning-based flare forecasting models deployed in a simulated operational environment. Using Georgia State University's Space Weather Analytics for Solar Flares benchmark dataset (Angryk et al.…

The solar dynamo is essentially a cyclic process in which the toroidal component of the magnetic field is converted into the poloidal one and vice versa. This cyclic loop is disturbed by some nonlinear and stochastic processes mainly…

Natural systems are typically nonlinear and complex, and it is of great interest to be able to reconstruct a system in order to understand its mechanism, which can not only recover nonlinear behaviors but also predict future dynamics. Due…

A functional time series approach is proposed for investigating spatial correlation in daily maximum temperature forecast errors for 111 cities spread across the U.S. The modelling of spatial correlation is most fruitful for longer forecast…

Solar flares, as one of the most prominent manifestations of solar activity, have a profound impact on both the Earth's space environment and human activities. As a result, accurate solar flare prediction has emerged as a central topic in…

The integration of renewable resources has increased in power generation as a means to reduce the fossil fuel usage and mitigate its adverse effects on the environment. However, renewables like solar energy are stochastic in nature due to…