# Deep Neural Networks for Nonlinear Model Order Reduction of Unsteady Flows

arXiv: https://arxiv.org/abs/2007.00936 · HTML: https://mlsanity.com/paper/2007.00936/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2020.

## Built on by (most cited first, 30 of 36)

- [Predicting Physics in Mesh-reduced Space with Temporal Attention](https://mlsanity.com/paper/2201.09113/) (2022)
- [β-Variational autoencoders and transformers for reduced-order modelling of fluid flows](https://mlsanity.com/paper/2304.03571/) (2023)
- [Towards extraction of orthogonal and parsimonious non-linear modes from turbulent flows](https://mlsanity.com/paper/2109.01514/) (2021)
- [Machine Learning in Aerodynamic Shape Optimization](https://mlsanity.com/paper/2202.07141/) (2022)
- [A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modeling](https://mlsanity.com/paper/2110.03442/) (2021)
- [Physics-aware Reduced-order Modeling of Transonic Flow via β-Variational Autoencoder](https://mlsanity.com/paper/2205.00608/) (2022)
- [CD-ROM: Complemented Deep-Reduced Order Model](https://mlsanity.com/paper/2202.10746/) (2022)
- [Dynamics of a data-driven low-dimensional model of turbulent minimal Couette flow](https://mlsanity.com/paper/2301.04638/) (2023)
- [State estimation with limited sensors -- A deep learning based approach](https://mlsanity.com/paper/2101.11513/) (2021)
- [Generative Adversarial Reduced Order Modelling](https://mlsanity.com/paper/2305.15881/) (2023)
- [Data-driven peakon and periodic peakon travelling wave solutions of some nonlinear dispersive equations via deep learning](https://mlsanity.com/paper/2101.04371/) (2021)
- [Interpretable A-posteriori Error Indication for Graph Neural Network Surrogate Models](https://mlsanity.com/paper/2311.07548/) (2023)
- [Towards aerodynamic surrogate modeling based on β-variational autoencoders](https://mlsanity.com/paper/2408.04969/) (2024)
- [Adaptive learning of effective dynamics: Adaptive real-time, online modeling for complex systems](https://mlsanity.com/paper/2304.01732/) (2023)
- [Deep learning for surrogate modelling of 2D mantle convection](https://mlsanity.com/paper/2108.10105/) (2021)
- [An AI-based Domain-Decomposition Non-Intrusive Reduced-Order Model for Extended Domains applied to Multiphase Flow in Pipes](https://mlsanity.com/paper/2202.06170/) (2022)
- [Data-driven Nonlinear Parametric Model Order Reduction Framework using Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2307.06816/) (2023)
- [Machine Learning based Prediction of Ditching Loads](https://mlsanity.com/paper/2402.10724/) (2024)
- [Data-driven reduced order modeling of environmental hydrodynamics using deep autoencoders and neural ODEs](https://mlsanity.com/paper/2107.02784/) (2021)
- [Mitigating distribution shift in machine learning-augmented hybrid simulation](https://mlsanity.com/paper/2401.09259/) (2024)
- [Polytopic Autoencoders with Smooth Clustering for Reduced-order Modelling of Flows](https://mlsanity.com/paper/2401.10620/) (2024)
- [Multi-Fidelity Bayesian Neural Network for Uncertainty Quantification in Transonic Aerodynamic Loads](https://mlsanity.com/paper/2407.05684/) (2024)
- [Learning Effective Dynamics across Spatio-Temporal Scales of Complex Flows](https://mlsanity.com/paper/2502.07990/) (2025)
- [Disentangled Latent Spaces for Reduced Order Models using Deterministic Autoencoders](https://mlsanity.com/paper/2502.14679/) (2025)
- [Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems](https://mlsanity.com/paper/2505.18857/) (2025)
- [Differentiable Autoencoding Neural Operator for Interpretable and Integrable Latent Space Modeling](https://mlsanity.com/paper/2510.00233/) (2025)
- [Control of Two-way Coupled Fluid Systems with Differentiable Solvers](https://mlsanity.com/paper/2206.00342/) (2022)
- [Systematic construction of continuous-time neural networks for linear dynamical systems](https://mlsanity.com/paper/2403.16215/) (2024)
- [Bridging Autoencoders and Dynamic Mode Decomposition for Reduced-order Modeling and Control of PDEs](https://mlsanity.com/paper/2409.06101/) (2024)
- [Data-driven system identification using quadratic embeddings of nonlinear dynamics](https://mlsanity.com/paper/2501.08202/) (2025)

## Abstract (arXiv)

Unsteady fluid systems are nonlinear high-dimensional dynamical systems that may exhibit multiple complex phenomena both in time and space. Reduced Order Modeling (ROM) of fluid flows has been an active research topic in the recent decade with the primary goal to decompose complex flows to a set of features most important for future state prediction and control, typically using a dimensionality reduction technique. In this work, a novel data-driven technique based on the power of deep neural networks for reduced order modeling of the unsteady fluid flows is introduced. An autoencoder network is used for nonlinear dimension reduction and feature extraction as an alternative for singular value decomposition (SVD). Then, the extracted features are used as an input for long short-term memory network (LSTM) to predict the velocity field at future time instances. The proposed autoencoder-LSTM method is compared with non-intrusive reduced order models based on dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD). Moreover, an autoencoder-DMD algorithm is introduced for reduced order modeling, which uses the autoencoder network for dimensionality reduction rather than SVD rank truncation. Results show that the autoencoder-LSTM method is considerably capable of predicting fluid flow evolution, where higher values for coefficient of determination R2 are obtained using autoencoder-LSTM compared to other models.