# Slim multi-scale convolutional autoencoder-based reduced-order models for interpretable features of a complex dynamical system

arXiv: https://arxiv.org/abs/2501.03070 · HTML: https://mlsanity.com/paper/2501.03070/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 46 references that are in the map.
- First posted on arXiv 6 Jan 2025.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [The Effectiveness of Data Augmentation in Image Classification using Deep Learning](https://mlsanity.com/paper/1712.04621/) (2017)
- [Learning with Pseudo-Ensembles](https://mlsanity.com/paper/1412.4864/) (2014)
- [Visual Interpretability for Deep Learning: a Survey](https://mlsanity.com/paper/1802.00614/) (2018)
- [Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks](https://mlsanity.com/paper/1802.07486/) (2018)
- [POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition](https://mlsanity.com/paper/2101.11845/) (2021)
- [Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems](https://mlsanity.com/paper/1808.01346/) (2018)
- [ALIME: Autoencoder Based Approach for Local Interpretability](https://mlsanity.com/paper/1909.02437/) (2019)
- [Synthetic Lagrangian Turbulence by Generative Diffusion Models](https://mlsanity.com/paper/2307.08529/) (2023)
- [An autoencoder-based reduced-order model for eigenvalue problems with application to neutron diffusion](https://mlsanity.com/paper/2008.10532/) (2020)
- [Analysis of dropout learning regarded as ensemble learning](https://mlsanity.com/paper/1706.06859/) (2017)
- [Reservoir computing model of two-dimensional turbulent convection](https://mlsanity.com/paper/2001.10280/) (2020)
- [Flipped Classroom: Effective Teaching for Time Series Forecasting](https://mlsanity.com/paper/2210.08959/) (2022)
- [Nonlinear proper orthogonal decomposition for convection-dominated flows](https://mlsanity.com/paper/2110.08295/) (2021)
- [Direct data-driven forecast of local turbulent heat flux in Rayleigh-B'enard convection](https://mlsanity.com/paper/2202.13129/) (2022)
- [Convolutional Autoencoders, Clustering and POD for Low-dimensional Parametrization of Navier-Stokes Equations](https://mlsanity.com/paper/2302.01278/) (2023)

## Abstract (arXiv)

In recent years, data-driven deep learning models have gained significant interest in the analysis of turbulent dynamical systems. Within the context of reduced-order models (ROMs), convolutional autoencoders (CAEs) pose a universally applicable alternative to conventional approaches. They can learn nonlinear transformations directly from data, without prior knowledge of the system. However, the features generated by such models lack interpretability. Thus, the resulting model is a black-box which effectively reduces the complexity of the system, but does not provide insights into the meaning of the latent features. To address this critical issue, we introduce a novel interpretable CAE approach for high-dimensional fluid flow data that maintains the reconstruction quality of conventional CAEs and allows for feature interpretation. Our method can be easily integrated into any existing CAE architecture with minor modifications of the training process. We compare our approach to Proper Orthogonal Decomposition (POD) and two existing methods for interpretable CAEs. We apply all methods to three different experimental turbulent Rayleigh-B'enard convection datasets with varying complexity. Our results show that the proposed method is lightweight, easy to train, and achieves relative reconstruction performance improvements of up to 6.4% over POD for 64 modes. The relative improvement increases to up to 229.8% as the number of modes decreases. Additionally, our method delivers interpretable features similar to those of POD and is significantly less resource-intensive than existing CAE approaches, using less than 2% of the parameters. These approaches either trade interpretability for reconstruction performance or only provide interpretability to a limited extend.