A twin-decoder structure for incompressible laminar flow reconstruction with uncertainty estimation around 2D obstacles

Over the past few years, deep learning methods have proved to be of great interest for the computational fluid dynamics community, especially when used as surrogate models, either for flow reconstruction, turbulence modeling, or for the prediction of aerodynamic coefficients. Overall exceptional levels of accuracy have been obtained but the robustness and reliability of the proposed approaches remain to be explored, particularly outside the confidence region defined by the training dataset. In this contribution, we present an autoencoder architecture with twin decoder for incompressible laminar flow reconstruction with uncertainty estimation around 2D obstacles. The proposed architecture is trained over a dataset composed of numerically-computed laminar flows around 12,000 random shapes, and naturally enforces a quasi-linear relation between a geometric reconstruction branch and the flow prediction decoder. Based on this feature, two uncertainty estimation processes are proposed, allowing either a binary decision (accept or reject prediction), or proposing a confidence interval along with the flow quantities prediction (u, v, p). Results over dataset samples as well as unseen shapes show a strong positive correlation of this reconstruction score to the mean-squared error of the flow prediction. Such approaches offer the possibility to warn the user of trained models when provided input shows too large deviation from the training data, making the produced surrogate model conservative for fast and reliable flow prediction.

Automated summary

Deep learning methods have shown great potential in computational fluid dynamics for flow reconstruction, turbulence modeling, and aerodynamic coefficient prediction. This study proposes an autoencoder architecture for incompressible laminar flow reconstruction with uncertainty estimation using a twin decoder. The architecture is trained on a dataset of 12,000 numerically-computed laminar flows around random shapes and provides two uncertainty estimation processes, allowing for binary decision or confidence interval prediction. Results demonstrate a strong positive correlation between the reconstruction score and the mean-squared error of flow prediction. This approach offers a conservative and reliable surrogate model for flow prediction, providing users with warnings for input deviations from the training data.