Resampling with neural networks for stochastic parameterization in multiscale systems

Daan Crommelin,Wouter Edeling

doi:10.1016/j.physd.2021.132894

Daan Crommelin, Wouter Edeling

Open Access

https://doi.org/10.1016/j.physd.2021.132894

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Abstract

In simulations of multiscale dynamical systems, not all relevant processes can be resolved explicitly. Taking the effect of the unresolved processes into account is important, which introduces the need for parameterizations. We present a machine-learning method, used for the conditional resampling of observations or reference data from a fully resolved simulation. It is based on the probabilistic classification of subsets of reference data, conditioned on macroscopic variables. This method is used to formulate a parameterization that is stochastic, taking the uncertainty of the unresolved scales into account. We validate our approach on the Lorenz 96 system, using two different parameter settings which are challenging for parameterization methods.

Highlights

For modeling and simulation of multiscale systems, a central problem is how to represent processes with small spatial scales and/or fast timescales
We presented a machine-learning method for the conditional resampling of subgrid-scale data of multiscale dynamical systems, resulting in a stochastic parameterization for the unresolved scales
The current model is comprised of a feed-forward architecture with softmax layers attached to the output

Summary

Introduction

For modeling and simulation of multiscale systems, a central problem is how to represent processes with small spatial scales and/or fast timescales. For many problems, the model output of interest involves only large-scale model variables, a natural approach to make simulations less expensive is to derive reduced models for the largescale variables only. We focus on data-driven approaches, where data of (the effect of) small-scale processes is used to infer a parameterization Data-driven methods can be useful when there is no clear separation between small/fast scales and large/slow scales, so that analytical or computational approaches that rely on such a scale gap do not apply

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