Multi-level stochastic refinement for complex time series and fields: A Data-Driven Approach

TL;DR

This paper introduces a hierarchical, data-driven method for generating synthetic multi-scale time series and fields that replicate the statistical features of complex spatio-temporal systems, demonstrated on turbulence data.

Contribution

It presents a novel multi-level stochastic refinement technique using transition PDFs to produce large synthetic datasets from limited measurements or simulations.

Findings

Successfully reproduces statistical multi-scale features of turbulence

Generates arbitrarily large synthetic datasets from experimental data

Validates approach with high Reynolds number turbulence data

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.