Using Machine Learning to predict extreme events in the Hénon map
Machine Learning (ML) inspired algorithms provide a flexible set of tools for analyzing and forecasting chaotic dynamical systems. We here analyze the performance of one algorithm for the prediction of extreme events in the two-dimensional H\'enon map at the classical parameters. The task is to determine whether a trajectory will exceed a threshold after a set number of time steps into the future. This task has a geometric interpretation within the dynamics of the H\'enon map, which we use to gauge the performance of the neural networks that are used in this work. We analyze the dependence of the success rate of the ML models on the prediction time $T$ , the number of training samples $N_T$ and the size of the network $N_p$. We observe that in order to maintain a certain accuracy, $N_T \propto exp(2 h T)$ and $N_p \propto exp(hT)$, where $h$ is the topological entropy. Similar relations between the intrinsic chaotic properties of the dynamics and ML parameters might be observable in other systems as well.
Code (0)
등록된 구현이 없습니다.
Tasks
BIG-bench Machine LearningSimilar Papers 제목 키워드 기반
Prediction of Occurrence of Extreme Events using Machine Learning
Machine learning models play a vital role in the prediction task in several fields of study. In this work, we utilize the ability of machine learning algorithms to predict the occurrence of extreme events in a nonlinear …
BIG-bench Machine LearningPredictionA physics-aware machine to predict extreme events in turbulence
We propose a physics-aware machine learning method to time-accurately predict extreme events in a turbulent flow. The method combines two radically different approaches: empirical modelling based on reservoir computing, …
Predicting extreme events from data using deep machine learning: when and where
We develop a deep convolutional neural network (DCNN) based framework for model-free prediction of the occurrence of extreme events both in time ("when") and in space ("where") in nonlinear physical systems of spatial di…
BIG-bench Machine LearningPredictionInductive Predictions of Extreme Hydrologic Events in The Wabash River Watershed
We present a machine learning method to predict extreme hydrologic events from spatially and temporally varying hydrological and meteorological data. We used a timestep reduction technique to reduce the computational and…
Time SeriesTime Series AnalysisOutput-weighted and relative entropy loss functions for deep learning precursors of extreme events
Many scientific and engineering problems require accurate models of dynamical systems with rare and extreme events. Such problems present a challenging task for data-driven modelling, with many naive machine learning met…