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Multi-level stochastic refinement for complex time series and fields: a data-driven approach

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Sinhuber,  Michael
Max Planck Research Group Theory of Turbulent Flows, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Wilczek,  Michael
Max Planck Research Group Theory of Turbulent Flows, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Sinhuber, M., Friedrich, J., Grauer, R., & Wilczek, M. (2021). Multi-level stochastic refinement for complex time series and fields: a data-driven approach. New Journal of Physics, 23: 063063. doi:10.1088/1367-2630/abe60e.


Cite as: https://hdl.handle.net/21.11116/0000-0007-535A-7
Abstract
Spatio-temporally extended nonlinear systems often exhibit a remarkable complexity in space and time. In many cases, extensive datasets of such systems are difficult to obtain, yet needed for a range of applications. Here, we present a method to generate synthetic time series or fields that reproduce statistical multi-scale features of complex systems. The method is based on a hierarchical refinement employing transition probability density functions (PDFs) from one scale to another. We address the case in which such PDFs can be obtained from experimental measurements or simulations and then used to generate arbitrarily large synthetic datasets. The validity of our approach is demonstrated at the example of an experimental dataset of high Reynolds number turbulence.