# Learning-based Reduced Order Model Stabilization for Partial Differential Equations: Application to the Coupled Burgers Equation

arXiv: https://arxiv.org/abs/1510.01728 · HTML: https://mlsanity.com/paper/1510.01728/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2015.

## Built on by (most cited first, 1 of 1)

- [Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning](https://mlsanity.com/paper/2202.05750/) (2022)

## Abstract (arXiv)

We present results on stabilization for reduced order models (ROM) of partial differential equations using learning. Stabilization is achieved via closure models for ROMs, where we use a model-free extremum seeking (ES) dither-based algorithm to learn the best closure models' parameters, for optimal ROM stabilization. We first propose to auto-tune linear closure models using ES, and then extend the results to a closure model combining linear and nonlinear terms, for better stabilization performance. The coupled Burgers' equation is employed as a test-bed for the proposed tuning method.