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

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