Performance and accuracy assessments of an incompressible fluid solver coupled with a deep convolutional neural network

Abstract

The resolution of the Poisson equation is usually one of the most computationally intensive steps for incompressible fluid solvers. Lately, DeepLearning, and especially convolutional neural networks (CNNs), has been introduced to solve this equation, leading to significant inference time reduction at the cost of a lack of guarantee on the accuracy of the solution.This drawback might lead to inaccuracies, potentially unstable simulations and prevent performing fair assessments of the CNN speedup for different network architectures. To circumvent this issue, a hybrid strategy is developed, which couples a CNN with a traditional iterative solver to ensure a user-defined accuracy level. The CNN hybrid method is tested on two flow cases: (a) the flow around a 2D cylinder and (b) the variable-density plumes with and without obstacles (both 2D and 3D), demonstrating remarkable generalization capabilities, ensuring both the accuracy and stability of the simulations. The error distribution of the predictions using several network architectures is further investigated in the plume test case. The introduced hybrid strategy allows a systematic evaluation of the CNN performance at the same accuracy level for various network architectures. In particular, the importance of incorporating multiple scales in the network architecture is demonstrated, since improving both the accuracy and the inference performance compared with feedforward CNN architectures. Thus, in addition to the pure networks’ performance evaluation, this study has also led to numerous guidelines and results on how to build neural networks and computational strategies to predict unsteady flows with both accuracy and stability requirements.

Spatiotemporal estimation of groundwater and surface water conditions by integrating deep learning and physics-based watershed models

“…A CNN is a type of DL algorithm specialized in capturing spatiotemporal features from multi-dimensional data ( Ajuria Illarramendi et al, 2022 ; LeCun et al, 2015 ). The convolutional filters and local connectivity in CNNs facilitate a better capture of the influence of the local features of the input data on the results ( Liao et al, 2023 ).…”

Discovering optimal flapping wing kinematics using active deep learning

“…Ajuria-Illaramendi et al. (2022) also revealed that using LTL improves the robustness and generalisation capabilities of the temporal predictions made by neural networks for operating conditions far from those used during training. Here, we chose to use simpler MLPs with a time delay in the input, as they are less expensive and easier to implement and train than LSTM networks or RNNs.…”

“…While such an approach has shown promising results, difficulties still exist, especially for long-time predictions. To tackle this issue while avoiding the complexity of recurrent networks, the learning of shift operators with short input history has been improved using long-term losses (LTLs), first introduced by Tompson et al (2017) and further exploited by Ajuria-Illaramendi, Bauerheim & Cuenot (2022) and Colombo et al (2023). The main idea is to collect during training new data by advancing in time the current network, and compare the predictions with the database.…”

“…To tackle this issue while avoiding the complexity of recurrent networks, the learning of shift operators with short input history has been improved using long-term losses (LTLs), first introduced by Tompson et al. (2017) and further exploited by Ajuria-Illaramendi, Bauerheim & Cuenot (2022) and Colombo et al. (2023).…”

Performance and accuracy assessments of an incompressible fluid solver coupled with a deep convolutional neural network—ADDENDUM

“…The editors and publisher of Data-Centric Engineering would like to include the Open Data badge in this article Ajuria Illarramendi E, et al (2022).…”