# Reduced-order modeling of unsteady fluid flow using neural network ensembles

arXiv: https://arxiv.org/abs/2402.05372 · HTML: https://mlsanity.com/paper/2402.05372/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 48 references that are in the map.
- First posted on arXiv 8 Feb 2024.

## Builds on (most cited first, 14 of 14)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [β-Variational autoencoders and transformers for reduced-order modelling of fluid flows](https://mlsanity.com/paper/2304.03571/) (2023)
- [Multi-level Convolutional Autoencoder Networks for Parametric Prediction of Spatio-temporal Dynamics](https://mlsanity.com/paper/1912.11114/) (2019)
- [Towards extraction of orthogonal and parsimonious non-linear modes from turbulent flows](https://mlsanity.com/paper/2109.01514/) (2021)
- [Residual-based physics-informed transfer learning: A hybrid method for accelerating long-term CFD simulations via deep learning](https://mlsanity.com/paper/2206.06817/) (2022)
- [XLB: A differentiable massively parallel lattice Boltzmann library in Python](https://mlsanity.com/paper/2311.16080/) (2023)
- [On the stability of projection-based model order reduction for convection-dominated laminar and turbulent flows](https://mlsanity.com/paper/2001.10110/) (2020)
- [A non-intrusive reduced order modeling framework for quasi-geostrophic turbulence](https://mlsanity.com/paper/1906.11617/) (2019)

## Built on by (most cited first, 4 of 4)

- [Physics-informed Reduced Order Modeling of Time-dependent PDEs via Differentiable Solvers](https://mlsanity.com/paper/2505.14595/) (2025)
- [Beyond the Kolmogorov Barrier: A Learnable Weighted Hybrid Autoencoder for Model Order Reduction](https://mlsanity.com/paper/2410.18148/) (2024)
- [Long-horizon prediction of three-dimensional wall-bounded turbulence with CTA-Swin-UNet and resolvent analysis](https://mlsanity.com/paper/2605.17888/) (2026)
- [Periodic Neural Mapping for Unsteady Rotor-Blade Pressure and Aeroelastic Load Prediction](https://mlsanity.com/paper/2609.21590/) (2026)

## Abstract (arXiv)

The use of deep learning has become increasingly popular in reduced-order models (ROMs) to obtain low-dimensional representations of full-order models. Convolutional autoencoders (CAEs) are often used to this end as they are adept at handling data that are spatially distributed, including solutions to partial differential equations. When applied to unsteady physics problems, ROMs also require a model for time-series prediction of the low-dimensional latent variables. Long short-term memory (LSTM) networks, a type of recurrent neural network useful for modeling sequential data, are frequently employed in data-driven ROMs for autoregressive time-series prediction. When making predictions at unseen design points over long time horizons, error propagation is a frequently encountered issue, where errors made early on can compound over time and lead to large inaccuracies. In this work, we propose using bagging, a commonly used ensemble learning technique, to develop a fully data-driven ROM framework referred to as the CAE-eLSTM ROM that uses CAEs for spatial reconstruction of the full-order model and LSTM ensembles for time-series prediction. When applied to two unsteady fluid dynamics problems, our results show that the presented framework effectively reduces error propagation and leads to more accurate time-series prediction of latent variables at unseen points.