# Extreme learning machine for reduced order modeling of turbulent geophysical flows

## TL;DR

This paper introduces an extreme learning machine-based method to enhance reduced order models of turbulent geophysical flows, significantly reducing computational costs while maintaining accuracy over long simulations.

## Contribution

It presents a novel neural network approach for dynamically computing eddy-viscosity closures in reduced order models of turbulent flows.

## Key findings

- Significant reduction in computational time.
- Effective retention of full-order model dynamics.
- Robust performance for larger time steps.

## Abstract

We investigate the application of artificial neural networks to stabilize proper orthogonal decomposition based reduced order models for quasi-stationary geophysical turbulent flows. An extreme learning machine concept is introduced for computing an eddy-viscosity closure dynamically to incorporate the effects of the truncated modes. We consider a four-gyre wind-driven ocean circulation problem as our prototype setting to assess the performance of the proposed data-driven approach. Our framework provides a significant reduction in computational time and effectively retains the dynamics of the full-order model during the forward simulation period beyond the training data set. Furthermore, we show that the method is robust for larger choices of time steps and can be used as an efficient and reliable tool for long time integration of general circulation models.