Deep Neural Networks for CFD Simulations

Research topic and goals

Simulation-based optimization in engineering requires high computational power and may benefit from system heterogeneity. Highly scalable CFD solvers have been developed at R-CCS, JSC, and BSC to conduct large-scale simulations. R-CCS focuses on full-scale simulations of vehicles aerodynamics. JSC and BSC investigate respiratory flows to improve medical treatments. Due to massive amounts of data produced, the analysis of the results is becoming a time-consuming process. Data-driven approaches have the potential to speed up analyses or to even replace certain physics in simulations. Deep learning methods have proven to be a fast alternative to extract multi-scale features from high-dimensional data sets. Deep neural networks (DNN) are able to predict the steady-state flow and aerodynamic coefficients around bluff bodies and airfoils, and unsteady laminar vortex shedding over circular bodies. Autoencoders (AE) or generative models, like variational AEs or generative adversarial networks (GANs), have shown great potential in predicting 2D and 3D flow fields.

It is the aim of the proposed cooperation to tie in with these topics and to develop methods to efficiently compute and analyze complex optimization setups in engineering utilizing heterogeneous architectures. The joint project focuses on the following three activities:

• The first activity concentrates on machine learning (ML)-based reduced order models (ROM) for the reconstruction of flow fields. Conventional linear ROM approaches, e.g., proper orthogonal decomposition (POD), cannot successfully reproduce the the nonlinear behavior of high Reynolds number (Re) flow fields. To address this problem, recently, nonlinear ROMs based on neural networks are attracting attention and are studied within this project.
• The second activity involves physics-informed neural networks (PINNs) for the prediction of flow fields. PINNs integrate the physical laws based on the governing equations along with constraints given by initial and boundary conditions in the loss function of a DNN. In the current project, they are trained with sparse spatial and/or temporal data of a computational domain to predict flow fields of the complete domain. The developments will be used for predicting flow based on sparse data from experimental fluid dynamics, e.g., the sparse pressure and velocity distributions at the surface of a road vehicle.
• The third activity focuses on flow predictions with graph neural networks (GNNs). GNNs can be applied to any shape or volume represented by a graph, e.g., triangulated shapes, or computational grids. Convolutional filters in GNNs operate on nodes and their neighboring nodes. This allows a more efficient training compared to convolutional neural networks (CNNs), whose convolutional filters are rectangular and operate in Cartesian directions. In this project, GNNs are trained with varying geometries of a flow configuration to predict the flow fields in new geometries that have not been part of the training data. The networks are developed for two types of training strategies: (i) in a supervised data-driven manner with ground truth data coming from CFD simulations and (ii) in an unsupervised data-free manner, where the network is guided with physical loss functions towards physically correct flow fields.

Bilateral support activities will lead to knowledge exchange with respect to the different hardware available at the partners’ sites, in CFD methods, and in deep learning approaches. Hence, expertise of the centers in these fields are strongly promoted in the course of this project. To foster the cooperation, mutual short-time stays of the involved scientists are planned.

Results for 2019/2020

None.

Results for 2020/2021

Due to the CODID-19 pandemic, the activities in the project had to be reduced. Unfortunately, a planned research stay of JSC’s Ph.D. student Mario Rüttgers at R-CCS could not take place. An exchange of research ideas took, however, place online via video conferences (see Visits and meetings below).

JSC was able to continue its work on DNNs. The architecture for such a neural network was developed to predict the sound pressure level in a 2D square domain. It was trained by numerical results from up to 20,000 GPU-based lattice-Boltzmann simulations that include randomly distributed rectangular and circular objects, and monopole sources. Types of boundary conditions, the monopole locations, and cell distances for objects and monopoles serve as input to the network. Parameters were studied to tune the predictions and to increase their accuracy. An optimal choice of the parameters lead to network-predicted results that are in good agreement with the simulated findings. The results have been presented at the International Conference on High Performance Computing - ISC High Performance 2020. A peer-reviewed article has been published in the corresponding Springer series as part of the Lecture Notes in Computer Science (LNCS)(Rüttgers et al. 2020).

R-CCS contributed with their talk “Distributed Learning for Three-dimensional Flow Field Mode Decomposition on Fugaku” to the 34th Computational Fluid Dynamics Symposium, which was held online on Dec. 21-23, 2020 (K. Ando, K. Onishi, R. Bale, M. Tsubokura, A. Kuroda, and K. Minami). In their research, R-CCS developed and investigated non-linear CNN-based mode decompositioning methods for three-dimensional flow fields around circular cylinder configurations. For the distributed learning, up to 25,250 nodes (1,212,000 cores) on the supercomputer Fugaku were used. Scalable model parallelization techniques for auto-encoder neural networks with a sustained performance of 7.8PFLOPs on 25,250 nodes were implemented.

Results for 2021/2022

The still ongoing pandemic lead again to reduced project activities. Nevertheless, both groups from JSC and R-CCS were able to continue their research.

JSC mainly worked on developing and integrating novel AI technologies into their CFD workflows. Reinforcement learning (RL) was implemented for shape optimization problems. For a generic case, i.e., a 2D channel with a constriction, RL was used to satisfy an optimum criterion that is a function of the pressure loss in the channel and the increase of the temperature given by the heat transfer at the channel wall. The work was presented at the International Conference on High Performance Computing - ISC High Performance 2021. A peer-reviewed article was published in the corresponding Springer series as part of the Lecture Notes in Computer Science (LNCS)(Rüttgers et al. 2021). An application of this technique to the shape optimization of a human nasal cavity is currently ongoing. At the JLESC meeting in 02/2021, the results of automating CFD workflows with a focus on the application to nasal cavity simulation workflows was presented. These results were later integrated into a journal article (Rüttgers et al. 2022).

R-CCS continued their work on developing DNNs for mode decompositioning of flow fields. They also participated in the International Conference on High Performance Computing - ISC High Performance 2021, with a talk “Nonlinear Mode Decomposition and Reduced-Order Modeling for Three-Dimensional Cylinder Flow by Distributed Learning on Fugaku”. They used CNNs to perform a parallel mode decompositioning of the flow field and employed long short-term memory networks (LSTMs) to predict the temporal development of the flow via the modes. The performance of this method was evaluated for different numbers of modes. A peer-reviewed article was published in the corresponding Springer series as part of the Lecture Notes in Computer Science (LNCS)(Ando et al. 2021)

Results for 2022/2023

Rakesh Sarma and Rishabh Puri joined the JLESC activities from the JSC side, and Onishi Junya from the R-CCS side. JSC and R-CCS jointly developed PINNs for flow predictions in classical problems of fluid dynamics, i.e., Poisueille flow, potential flow, Blasius boundary layer flow, and the Taylor-Green vortex. Rhishabh Puri presented the results at the Platform for Advanced Scientific Computing 2023 (PASC23) conference in Davos, Switzerland.

JSC and R-CCS jointly developed a GNN for the prediction of flow around air foils. The GNN uses computational grids of the simulation framework “multiphysics-Aerodynamisches Institut Aachen” (m-AIA), an extended version of the formerly known “Zonal Flow Solver”(Lintermann, Meinke, and Schröder 2020), and automatically generates an adjacency matrix that contains information about nodes and neighbouring nodes. First steps have been initiated to develop an open access library for GNN-based flow predictions. The PINN and GNN activities were intensified by a research visit of Onishi Junya at JSC in August 2023.

Regarding the AI-based reduced-order model, in this fiscal year, the functionality of the model has been enhanced. That is, a variational autoencoder (VAE) has been integrated for outputting latent variables in the model. Due to this modification, the reduction performance was increased for turbulent flow simulation data. These results have been presented at the ParCFD2022 and WCCM2022 conferences.

Results for 2023/2024

Rishabh Puri starts his PhD programme at KIT, but continues the JLESC activities as an associated researcher. Hadrien Calmet joined the JLESC activities from the BSC side. After demonstrating the robustness of PINNs for flow predictions in classical flow problems, the activities regarding PINNs are extended to vehicle aerodynamics. That is, flow fields around a road vehicle are predicted based on sparse spatial data at the vehicles’s surface, to derive force coefficients such as drag or lift. In a first step, the sparse surface data are extracted from CFD simulations conducted by the R-CCS side, as discussed during a research visit of Mario Rüttgers at R-CCS in October 2023. After this proof-of-concept, the sparse surface data could stem from experimental measurements at a driving vehicle.

The activities regarding GNNs are extended to respiratory flows. Hadrien Calmet aims to investigate GNNs by initiating the first phase, which involves employing the existing 2D algorithm of Graph Convolutional Neural Networks (GCNN) (Ogoke et al. 2021) and evaluating its efficacy with a 3D dataset. The goal is to predict respiratory system flow features such as air resistance, wall shear stress, and energy flux within the human nasal cavity during inspiration. The initial step involves generating a virtual population through random scaling applied simultaneously to length, width, and height. Three distinct geometries are chosen, including an average one based on 35 healthy patients, a Caucasian healthy patient, and an Asian healthy patient. Once the neural network demonstrates satisfactory accuracy, a second phase is planned to assess the algorithm’s performance. This evaluation will utilize Paraver, a performance tool developed at BSC. Additionally, there is a consideration for the implementation of multi-GPU using PyTorch, allowing for a performance comparison. The final step involves testing the AI4HPC open-source library to train the dataset with the GNN algorithm and engaging in a discussion about the obtained results.

Regarding the AI-based reduced-order model, the scope of application is extended. First, the method is applied to the turbulent flow around a vehicle calculated with 260 million cells. Distributed training was conducted for over 14 hours using 55,000 Fugaku computing nodes. Since the model is still in the early stages of learning, small-period eddies could not yet be reproduced, but large-scale structure could be reconstructed. Second, the robustness of the model is addressed for a two-dimensional flow around two square cylinders, which have a varying distances. It is demonstrated that flow configurations that did not belong to the training data are successfully reproduced using 24 modes. It is planned to submit these results to the JLESC special issue of the journal “Future Generation Computer Systems”.

Visits and meetings

• throughout 2020: discussions of hosting a JSC researcher at R-CCS (canceled due to the COVID-19 pandemic)
• 02.12.2020: R-CCS presents latest work on mode decomposition using ML for 3D cylinder cases to JSC.
• 23.03.2020: JSC presents previous work in the combined field of CFD, AI to the JLESC partners at R-CCS (application of AI methods to automatize CFD workflows, ML-based segmentation of computer tomography images in preparation of CFD computations of respiratory flows, prediction of sound pressure level distributions with DNNs).
• 08.12.2020 - 11.12.2020: Meeting of the PIs Makoto Tsubokura, Andreas Lintermann, and the researchers Keiji Onishi (R-CCS) and Mario Rüttgers in the framework of the COMPSAFE 2020 online conference.
• 24.02.2021 - 26.02.2021: Mario Rüttgers presents the jointly developed results at the 13th JLESC workshop, online.
• 04.07.2022 - 06.07.2022: Mario Rüttgers presents the jointly developed results at the Kobe Opportunities workshop organized by Makoto Tsubokura in Brussels, Belgium.
• 28.09.2022 - 30.09.2022: Mario Rüttgers presents the jointly developed results at the 14th JLESC workshop in Urbana-Champaign, USA.
• 21.03.2023 - 23.03.2023: Ando Kazuto presents the jointly developed results at the 15th JLESC workshop in Bordeaux, France.
• 03.07.2023 - 07.07.2023: Research exchange: Onishi Junya from R-CCS visits researchers from JSC at JSC.
• 24.10.2023 - 27.10.2023: Research exchange: Mario Rüttgers visits researchers from R-CCS at R-CCS.

Impact and publications

1. Ruttgers2022APIN

   BibTeX Abstract

   Rüttgers, Mario, Moritz Waldmann, Wolfgang Schröder, and Andreas Lintermann. 2022. “A Machine-Learning-Based Method for Automatizing Lattice-Boltzmann Simulations of Respiratory Flows.” Applied Intelligence, no. first online (January). https://doi.org/10.1007/s10489-021-02808-2.

   @article{Ruttgers2022APIN,
     author = {R{\"{u}}ttgers, Mario and Waldmann, Moritz and Schr{\"{o}}der, Wolfgang and Lintermann, Andreas},
     doi = {10.1007/s10489-021-02808-2},
     issn = {0924-669X},
     journal = {Applied Intelligence},
     month = jan,
     number = {first online},
     title = {{A machine-learning-based method for automatizing lattice-Boltzmann simulations of respiratory flows}},
     url = {https://link.springer.com/10.1007/s10489-021-02808-2},
     year = {2022}
   }
   

2. Ogoke2021

   BibTeX Abstract

   Ogoke, Francis, Kazem Meidani, Amirreza Hashemi, and Amir Barati Farimani. 2021. “Graph Convolutional Networks Applied to Unstructured Flow Field Data.” Machine Learning: Science and Technology 2 (September). https://doi.org/10.1088/2632-2153/ac1fc9.

   @article{Ogoke2021,
     author = {Ogoke, Francis and Meidani, Kazem and Hashemi, Amirreza and Barati Farimani, Amir},
     year = {2021},
     month = sep,
     pages = {},
     title = {Graph Convolutional Networks applied to unstructured flow field data},
     volume = {2},
     journal = {Machine Learning: Science and Technology},
     doi = {10.1088/2632-2153/ac1fc9}
   }
   

3. Ruttgers2021ISC

   BibTeX Abstract

   Rüttgers, Mario, Moritz Waldmann, Wolfgang Schröder, and Andreas Lintermann. 2021. “Machine-Learning-Based Control of Perturbed and Heated Channel Flows.” In High Performance Computing, Proceedings of the 36th International Conference, ISC High Performance 2021, 7–22. Frankfurt/Main, Germany: Springer International Publishing. https://doi.org/10.1007/978-3-030-90539-2_1.

   @incollection{Ruttgers2021ISC,
     address = {Frankfurt/Main, Germany},
     author = {R{\"{u}}ttgers, Mario and Waldmann, Moritz and Schr{\"{o}}der, Wolfgang and Lintermann, Andreas},
     booktitle = {High Performance Computing, Proceedings of the 36th International Conference, ISC High Performance 2021},
     doi = {10.1007/978-3-030-90539-2_1},
     pages = {7--22},
     publisher = {Springer International Publishing},
     title = {{Machine-Learning-Based Control of Perturbed and Heated Channel Flows}},
     url = {https://link.springer.com/10.1007/978-3-030-90539-2{\_}1},
     year = {2021}
   }
   

4. Ando2021ISC

   BibTeX Abstract

   Ando, Kazuto, Keiji Onishi, Rahul Bale, Makoto Tsubokura, Akiyoshi Kuroda, and Kazuo Minami. 2021. “Nonlinear Mode Decomposition and Reduced-Order Modeling for Three-Dimensional Cylinder Flow by Distributed Learning on Fugaku.” In High Performance Computing, Proceedings of the 36th International Conference, ISC High Performance 2021, 122–37. Frankfurt/Main, Germany: Springer International Publishing. https://doi.org/10.1007/978-3-030-90539-2_8.

   @incollection{Ando2021ISC,
     address = {Frankfurt/Main, Germany},
     author = {Ando, Kazuto and Onishi, Keiji and Bale, Rahul and Tsubokura, Makoto and Kuroda, Akiyoshi and Minami, Kazuo},
     booktitle = {High Performance Computing, Proceedings of the 36th International Conference, ISC High Performance 2021},
     doi = {10.1007/978-3-030-90539-2_8},
     pages = {122--137},
     publisher = {Springer International Publishing},
     title = {{Nonlinear Mode Decomposition and Reduced-Order Modeling for Three-Dimensional Cylinder Flow by Distributed Learning on Fugaku}},
     url = {https://link.springer.com/10.1007/978-3-030-90539-2{\_}8},
     year = {2021}
   }
   

5. Lintermann2020

   BibTeX Abstract

   Lintermann, Andreas, Matthias Meinke, and Wolfgang Schröder. 2020. “Zonal Flow Solver (ZFS): a Highly Efficient Multi- Physics Simulation Framework.” International Journal of Computational Fluid Dynamics 34 (March). https://doi.org/10.1080/10618562.2020.1742328.

   @article{Lintermann2020,
     author = {Lintermann, Andreas and Meinke, Matthias and Schröder, Wolfgang},
     year = {2020},
     month = mar,
     pages = {},
     title = {Zonal Flow Solver (ZFS): a highly efficient multi- physics simulation framework},
     volume = {34},
     journal = {International Journal of Computational Fluid Dynamics},
     doi = {10.1080/10618562.2020.1742328}
   }
   

6. Ruttgers2020

   BibTeX Abstract

   Rüttgers, Mario, Seong-Ryong Koh, Jenia Jitsev, Wolfgang Schröder, and Andreas Lintermann. 2020. “Prediction of Acoustic Fields Using a Lattice-Boltzmann Method and Deep Learning.” In High Performance Computing, Proceedings of the 35th International Conference, ISC High Performance 2020, 81–101. Frankfurt/Main, Germany: Springer International Publishing. https://doi.org/10.1007/978-3-030-59851-8_6.

   @incollection{Ruttgers2020,
     address = {Frankfurt/Main, Germany},
     author = {R{\"{u}}ttgers, Mario and Koh, Seong-Ryong and Jitsev, Jenia and Schr{\"{o}}der, Wolfgang and Lintermann, Andreas},
     booktitle = {High Performance Computing, Proceedings of the 35th International Conference, ISC High Performance 2020},
     doi = {10.1007/978-3-030-59851-8_6},
     pages = {81--101},
     publisher = {Springer International Publishing},
     title = {{Prediction of Acoustic Fields Using a Lattice-Boltzmann Method and Deep Learning}},
     url = {http://link.springer.com/10.1007/978-3-030-59851-8{\_}6},
     year = {2020}
   }
   

Future plans

Further intensification of the cooperation and planning of research stays for a post-pandemic phase.

References