Projekt Badawczy 2021/43/B/ST8/00641: Przewidywanie zdarzeń ekstremalnych w układach sprzężonych oscylatorów mechanicznych w oparciu o uczenie maszynowe

The primary objective of the project is to develop deep and rigorous understanding of a wide class of complex dynamical systems, generically represented by a homogeneous network of interconnected mechanical oscillators. These systems have been very recently explored through their unexpected processes of instabilities, such as; interior crisis, Pomeau–Manneville intermittency and the breakdown of quasiperiodic motion. These instabilities are most commonly observed in many systems and often cause the occasional and rare transitions to large amplitude spiking events, the so-called extreme events. Machine learning inspired algorithms provide a flexible set of tools for analyzing and forecasting complex dynamical systems. Here, we develop and analyze the performance of algorithms suitable for the prediction of extreme events in the networks of coupled oscillators. The corollary objective is to anticipate and transpose, thanks to the deep understanding of the mechanisms leading to extreme events, their implications in several well identified technological contexts. The ground-breaking potential of the project is a straightforward consequence of the recent discovery that extreme events and the related anomalous statistics are ubiquitously observed in many natural systems but the development of efficient methods to understand and accurately predict such representative features remains a grand challenge. Here, we assume that the recent progress in the development of machine learning algorithms will allow to apply such algorithms to predict extreme events in the network of coupled oscillators. Important and innovative impacts are expected because such identified situations and conditions for the emergence of extreme events can be closely connected to many not only technological (e.g. biological and social) problems. The research findings from this project are expected to trigger new paradigms in the management and design of complex systems in general, with breakthrough implications in technology. We anticipate that such novel phenomena can provide rigorous understanding of many yet unexplained observations. It will provide efficient but yet unknown and unexpected engineering design rules for future complex systems made of many interconnected technological elements. Unwanted, specific solutions defined as an extreme events could thus be predicted and/or controlled due to the understanding of the deterministic rules and mechanisms at the origin of the global behavior of a network-like system of complex interconnected individual elements.