# Combined space-time reduced-order model with 3D deep convolution for extrapolating fluid dynamics

arXiv: https://arxiv.org/abs/2211.00307 · HTML: https://mlsanity.com/paper/2211.00307/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 46 references that are in the map.
- First posted on arXiv 1 Nov 2022.

## Builds on (most cited first, 10 of 10)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Tune: A Research Platform for Distributed Model Selection and Training](https://mlsanity.com/paper/1807.05118/) (2018)
- [Inductive Biases for Deep Learning of Higher-Level Cognition](https://mlsanity.com/paper/2011.15091/) (2020)
- [Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems](https://mlsanity.com/paper/2003.04919/) (2020)
- [Deep Learning for Reduced Order Modelling and Efficient Temporal Evolution of Fluid Simulations](https://mlsanity.com/paper/2107.04556/) (2021)
- [Assessment of unsteady flow predictions using hybrid deep learning based reduced order models](https://mlsanity.com/paper/2009.04396/) (2020)
- [Kolmogorov n-widths for linear dynamical systems](https://mlsanity.com/paper/1806.09880/) (2018)
- [Predicting waves in fluids with deep neural network](https://mlsanity.com/paper/2201.06628/) (2022)

## Abstract (arXiv)

There is a critical need for efficient and reliable active flow control strategies to reduce drag and noise in aerospace and marine engineering applications. While traditional full-order models based on the Navier-Stokes equations are not feasible, advanced model reduction techniques can be inefficient for active control tasks, especially with strong non-linearity and convection-dominated phenomena. Using convolutional recurrent autoencoder network architectures, deep learning-based reduced-order models have been recently shown to be effective while performing several orders of magnitude faster than full-order simulations. However, these models encounter significant challenges outside the training data, limiting their effectiveness for active control and optimization tasks. In this study, we aim to improve the extrapolation capability by modifying network architecture and integrating coupled space-time physics as an implicit bias. Reduced-order models via deep learning generally employ decoupling in spatial and temporal dimensions, which can introduce modeling and approximation errors. To alleviate these errors, we propose a novel technique for learning coupled spatial-temporal correlation using a 3D convolution network. We assess the proposed technique against a standard encoder-propagator-decoder model and demonstrate a superior extrapolation performance. To demonstrate the effectiveness of 3D convolution network, we consider a benchmark problem of the flow past a circular cylinder at laminar flow conditions and use the spatio-temporal snapshots from the full-order simulations. Our proposed 3D convolution architecture accurately captures the velocity and pressure fields for varying Reynolds numbers. Compared to the standard encoder-propagator-decoder network, the spatio-temporal-based 3D convolution network improves the prediction range of Reynolds numbers outside of the training data.