# Investigation of Nonlinear Model Order Reduction of the Quasigeostrophic Equations through a Physics-Informed Convolutional Autoencoder

arXiv: https://arxiv.org/abs/2108.12344 · HTML: https://mlsanity.com/paper/2108.12344/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 36 references that are in the map.
- First posted on arXiv 27 Aug 2021.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling](https://mlsanity.com/paper/1710.11431/) (2017)
- [Forecasting Sequential Data using Consistent Koopman Autoencoders](https://mlsanity.com/paper/2003.02236/) (2020)
- [Deep Learning of Vortex Induced Vibrations](https://mlsanity.com/paper/1808.08952/) (2018)
- [Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction](https://mlsanity.com/paper/1905.10866/) (2019)
- [A Multifidelity Ensemble Kalman Filter with Reduced Order Control Variates](https://mlsanity.com/paper/2007.00793/) (2020)
- [Enforcing Deterministic Constraints on Generative Adversarial Networks for Emulating Physical Systems](https://mlsanity.com/paper/1911.06671/) (2019)
- [Multifidelity Ensemble Kalman Filtering Using Surrogate Models Defined by Physics-Informed Autoencoders](https://mlsanity.com/paper/2102.13025/) (2021)
- [POD/DEIM Reduced-Order Strategies for Efficient Four Dimensional Variational Data Assimilation](https://mlsanity.com/paper/1402.5992/) (2014)

## Built on by (most cited first, 2 of 2)

- [Adjoint-Matching Neural Network Surrogates for Fast 4D-Var Data Assimilation](https://mlsanity.com/paper/2111.08626/) (2021)
- [A Meta-learning Formulation of the Autoencoder Problem for Non-linear Dimensionality Reduction](https://mlsanity.com/paper/2207.06676/) (2022)

## Abstract (arXiv)

Reduced order modeling (ROM) is a field of techniques that approximates complex physics-based models of real-world processes by inexpensive surrogates that capture important dynamical characteristics with a smaller number of degrees of freedom. Traditional ROM techniques such as proper orthogonal decomposition (POD) focus on linear projections of the dynamics onto a set of spectral features. In this paper we explore the construction of ROM using autoencoders (AE) that perform nonlinear projections of the system dynamics onto a low dimensional manifold learned from data. The approach uses convolutional neural networks (CNN) to learn spatial features as opposed to spectral, and utilize a physics informed (PI) cost function in order to capture temporal features as well. Our investigation using the quasi-geostrophic equations reveals that while the PI cost function helps with spatial reconstruction, spatial features are less powerful than spectral features, and that construction of ROMs through machine learning-based methods requires significant investigation into novel non-standard methodologies.