# Reducing Spatial Discretization Error on Coarse CFD Simulations Using an OpenFOAM-Embedded Deep Learning Framework

arXiv: https://arxiv.org/abs/2405.07441 · HTML: https://mlsanity.com/paper/2405.07441/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 61 references that are in the map.
- First posted on arXiv 13 May 2024.

## Builds on (most cited first, 15 of 15)

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- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
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- [Deep Learning for Single Image Super-Resolution: A Brief Review](https://mlsanity.com/paper/1808.03344/) (2018)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [CFDNet: a deep learning-based accelerator for fluid simulations](https://mlsanity.com/paper/2005.04485/) (2020)
- [Deep Learning for Reduced Order Modelling and Efficient Temporal Evolution of Fluid Simulations](https://mlsanity.com/paper/2107.04556/) (2021)
- [Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flows](https://mlsanity.com/paper/2301.10937/) (2023)
- [Machine Learning for Partial Differential Equations](https://mlsanity.com/paper/2303.17078/) (2023)
- [Assessments of epistemic uncertainty using Gaussian stochastic weight averaging for fluid-flow regression](https://mlsanity.com/paper/2109.08248/) (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)
- [PythonFOAM: In-situ data analyses with OpenFOAM and Python](https://mlsanity.com/paper/2103.09389/) (2021)
- [A general approach for running Python codes in OpenFOAM using an embedded pybind11 Python interpreter](https://mlsanity.com/paper/2203.16394/) (2022)

## Abstract (arXiv)

We propose a method for reducing the spatial discretization error of coarse computational fluid dynamics (CFD) problems by enhancing the quality of low-resolution simulations using deep learning. We feed the model with fine-grid data after projecting it to the coarse-grid discretization. We substitute the default differencing scheme for the convection term by a feed-forward neural network that interpolates velocities from cell centers to face values to produce velocities that approximate the down-sampled fine-grid data well. The deep learning framework incorporates the open-source CFD code OpenFOAM, resulting in an end-to-end differentiable model. We automatically differentiate the CFD physics using a discrete adjoint code version. We present a fast communication method between TensorFlow (Python) and OpenFOAM (c++) that accelerates the training process. We applied the model to the flow past a square cylinder problem, reducing the error from 120% to 25% in the velocity for simulations inside the training distribution compared to the traditional solver using an x8 coarser mesh. For simulations outside the training distribution, the error reduction in the velocities was about 50%. The training is affordable in terms of time and data samples since the architecture exploits the local features of the physics.