Machine learning-based identification of precursors of extreme events in chaotic systems

Abrupt and rapid high-amplitude changes in a dynamical system’s states known as extreme events appear in many processes occurring in nature, such as drastic climate patterns, rogue waves, or avalanches. These events often entail catastrophic effects, therefore their description and prediction is of great importance. Nevertheless, because of...

On the Application of the Competitive Modes Conjecture

Modelling natural phenomena via Dynamical System Theory has become commonplace amongst mathematicians, physicists, engineers, and the like. As such, research in this field is currently underway, with a notable focus on chaos. The Competitive Modes Conjecture is a relatively new approach in the field of chaotic Dynamical Systems, aiming to...

Continuous-discrete smoothing of diffusions

Suppose X is a multivariate diffusion process that is observed discretely in time. At each observation time, a transformation of the state of the process is observed with noise. The smoothing problem consists of recovering the path of the process, consistent with the observations. We derive a novel Markov Chain Monte Carlo algorithm to sample...

Time Integration Parallel in Time

In this paper the research behind the parallelization on the GPU of the time parallel time integration method Parareal. Firstly, the theory behind Parareal and its convergence theorems will be detailed. Then, two test models, the Lorenz system and Heat diffusion equation, will be introduced. Additionally, the derivation of the Forward Euler and...