Statistical model of non-Gaussian process with wavelet scattering moments

Date(s) : 25/05/2018   iCal
14 h 00 min - 15 h 00 min

One of the most challenging problems in statistical modeling is to define a minimal set of statistics so as to infer a stochastic model from few observational data of the underlying random process.
We propose such set of statistics based on the wavelet scattering transform. Our goal is to model the non-Gaussianarity and the long-range interaction of the data, in particular when there is complex geometry and transient structures at multiple scales such as Turbulence. We follow the maximum entropy principle to infer a stochastic model given a set of statistical moment constraints. It results in a Gibbs distribution which is common in statistical physics to describe the equilibrium states. In this talk, I will discuss the current state-of-art methods to model the texture as a stationary and ergodic random process, including convolutional neural network based approach. We compare different methods quantitatively by estimating the power spectrum, and the entropy of the random process. Numerical results on isotropic Turbulence will be presented.

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