Towards data-driven dynamic surrogate models for ocean flow

Coarse graining of (geophysical) flow problems is a necessity brought upon us by the wide range of spatial and temporal scales present in these problems, which cannot be all represented on a numerical grid without an inordinate amount of computational resources. Traditionally, the effect of the unresolved eddies is approximated by deterministic closure models, i.e. so-called parameterizations. The effect of the unresolved eddy field enters the resolved-scale equations as a forcing term, denoted as the’eddy forcing’. Instead of creating a deterministic parameterization, our goal is to infer a stochastic, data-driven surrogate model for the eddy forcing from a (limited) set of reference data, with the goal of accurately capturing the long-term flow statistics. Our surrogate modelling approach essentially builds on a resampling strategy, where we create a probability density function of the reference data that is conditional on (time-lagged) resolved-scale variables. The choice of resolved-scale variables, as well as the employed time lag, is essential to the performance of the surrogate. We will demonstrate the effect of different modelling choices on a simplified ocean model of two-dimensional turbulence in a doubly periodic square domain

Fluctuation Analysis of the Atmospheric Energy Cycle

The atmosphere gains available potential energy by solar radiation and dissipates kinetic energy mainly in the atmospheric boundary layer. We analyze the fluctuations of the global mean energy cycle defined by Lorenz (1955) in a simulation with a simplified hydrostatic model. The energy current densities are well approximated by the generalized Gumbel distribution (Bramwell, Holdsworth and Pinton, 1998) and the Generalized Extreme Value (GEV) distribution. In an attempt to assess the fluctuation relation of Evans, Cohen, and Morriss (1993) we define entropy production by the injected power and use the GEV location parameter as a reference state. The fluctuation ratio reveals a linear behavior in a finite range.Comment: 17 pages, 5 figure

Reducing data-driven dynamical subgrid scale models by physical constraints

Recent years have seen a growing interest in using data-driven (machine-learning) techniques for the construction of cheap surrogate models of turbulent subgrid scale stresses. These stresses display complex spatio-temporal structures, and constitute a difficult surrogate target. In this paper we propose a data-preprocessing step, in which we derive alternative subgrid scale models which are virtually exact for a user-specified set of spatially integrated quantities of interest. The unclosed component of these new subgrid scale models is of the same size as this set of integrated quantities of interest. As a result, the corresponding training data is massively reduced in size, decreasing the complexity of the subsequent surrogate construction

Reduced order modeling of fluid flows: Machine learning, Kolmogorov barrier, closure modeling, and partitioning

In this paper, we put forth a long short-term memory (LSTM) nudging framework for the enhancement of reduced order models (ROMs) of fluid flows utilizing noisy measurements. We build on the fact that in a realistic application, there are uncertainties in initial conditions, boundary conditions, model parameters, and/or field measurements. Moreover, conventional nonlinear ROMs based on Galerkin projection (GROMs) suffer from imperfection and solution instabilities due to the modal truncation, especially for advection-dominated flows with slow decay in the Kolmogorov width. In the presented LSTM-Nudge approach, we fuse forecasts from a combination of imperfect GROM and uncertain state estimates, with sparse Eulerian sensor measurements to provide more reliable predictions in a dynamical data assimilation framework. We illustrate the idea with the viscous Burgers problem, as a benchmark test bed with quadratic nonlinearity and Laplacian dissipation. We investigate the effects of measurements noise and state estimate uncertainty on the performance of the LSTM-Nudge behavior. We also demonstrate that it can sufficiently handle different levels of temporal and spatial measurement sparsity. This first step in our assessment of the proposed model shows that the LSTM nudging could represent a viable realtime predictive tool in emerging digital twin systems