Data-driven methods for dynamical systems: Quantifying predictability and extracting spatiotemporal patterns
نویسندگان
چکیده
Large-scale datasets generated by dynamical systems arise in many applications in science and engineering. Two research topics of current interest in this area involve using data collected through observational networks or output by numerical models to quantify the uncertainty in long-range forecasting, and improve understanding of the operating dynamics. In this research expository we discuss applied mathematics techniques to address these topics blending ideas from machine learning, delay-coordinate embeddings of dynamical systems, and information theory. We illustrate these methods with applications to climate atmosphere ocean science.
منابع مشابه
The Heterogeneous Dynamics of Economic Complexity
What will be the growth of the Gross Domestic Product (GDP) or the competitiveness of China, United States, and Vietnam in the next 3, 5 or 10 years? Despite this kind of questions has a large societal impact and an extreme value for economic policy making, providing a scientific basis for economic predictability is still a very challenging problem. Recent results of a new branch--Economic Comp...
متن کاملCONTROL OF CHAOS IN A DRIVEN NON LINEAR DYNAMICAL SYSTEM
We present a numerical study of a one-dimensional version of the Burridge-Knopoff model [16] of N-site chain of spring-blocks with stick-slip dynamics. Our numerical analysis and computer simulations lead to a set of different results corresponding to different boundary conditions. It is shown that we can convert a chaotic behaviour system to a highly ordered and periodic behaviour by making on...
متن کاملSpatiotemporal Feature Extraction with Data-Driven Koopman Operators
We present a framework for feature extraction and mode decomposition of spatiotemporal data generated by ergodic dynamical systems. Unlike feature extraction techniques based on kernel operators, our approach is to construct feature maps using eigenfunctions of the Koopman group of unitary operators governing the dynamical evolution of observables and probability measures. We compute the eigenv...
متن کامل2 00 2 Local dimension and finite time prediction in spatiotemporal chaotic systems
We show how a recently introduced statistics [Patil et al, Phys. Rev. Lett. 81 5878 (2001)] provides a direct relationship between dimension and predictability in spatiotemporal chaotic systems. Regions of low dimension are identified as having high predictability and vice-versa. This conclusion is reached by using methods from dynamical systems theory and Bayesian modelling. We emphasize in th...
متن کاملA comparison between the Kazerun (Iran) and the North Anatolian (Turkey) fault systems in fault interaction and seismicity migration based on the spatiotemporal analysis of earthquakes
The Kazerun Fault System (KFS) is a right-lateral strike slip fault system in the middle part of the Zagros seismogenic zone in Iran. Historical and instrumental earthquake data catalogs of this fault system show good evidence of fault interactions and seismic migrations. This study provides evidence for the migration of seismicity in the middle part of the Zagros region along the segments of t...
متن کامل