# A non-intrusive reduced order modeling framework for quasi-geostrophic turbulence

## TL;DR

This paper introduces a non-intrusive reduced order modeling framework using LSTM neural networks for quasi-geostrophic turbulence, enabling stable, accurate predictions with fewer modes compared to traditional methods.

## Contribution

The study develops a novel ROM framework that leverages LSTM for efficient, stable, and accurate prediction of complex fluid flows with fewer modes than conventional projection-based ROMs.

## Key findings

- ROM-LSTM captures intermittent bursts accurately
- ROM-LSTM achieves stable solutions with fewer POD modes
- Outperforms traditional Galerkin projection ROMs in stability and efficiency

## Abstract

In this study, we present a non-intrusive reduced order modeling (ROM) framework for large-scale quasi-stationary systems. The framework proposed herein exploits the time series prediction capability of long short-term memory (LSTM) recurrent neural network such that: (i) in the training phase, the LSTM model is trained on the modal coefficients extracted from the high-resolution data using proper orthogonal decomposition (POD) transform, and (ii) in the testing phase, the trained model predicts the modal coefficients for the total time recursively based on the initial time history. To illustrate the predictive performance of the proposed framework, the mean flow fields and time series response of the field values are reconstructed from the predicted modal coefficients by using an inverse POD transform. As a representative benchmark test case, we consider a two-dimensional quasi-geostrophic (QG) ocean circulation model which, in general, displays an enormous range of fluctuating spatial and temporal scales. We first illustrate that the conventional Galerkin projection based ROM of such systems requires a high number of POD modes to obtain a stable flow physics. In addition, ROM-GP does not seem to capture the intermittent bursts appearing in the dynamics of the first few most energetic modes. However, the proposed non-intrusive ROM framework based on LSTM (ROM-LSTM) yields a stable solution even for a small number of POD modes. We also observe that the ROM-LSTM model is able to capture quasi-periodic intermittent bursts accurately, and yields a stable and accurate mean flow dynamics using the time history of a few previous time states, denoted as the lookback time-window in this paper. Our findings suggest that the proposed ROM framework is capable of predicting noisy nonlinear fluid flows in an extremely efficient way compared to the conventional projection based ROM.