Abstract
This paper presents a novel surrogate modeling method with physics constraints that is specifically designed for optimal design in flow control systems. The governing partial differential equations describing these flows are presented, considering a simplified fluid confined within a channel bounded by two parallel walls. Boundary conditions and flow control are introduced through geometric grooves and transpiration effects. The discretization of the governing equations and boundary conditions is also discussed. For numerical simulations, a Galerkin-based PDE solver is employed, utilizing spectral methods. The separation of Fourier components results in a system of ordinary differential equations for the modal functions. The effectiveness of transpiration in inducing flow control is evaluated by comparing the computed values with the reference pressure gradient required to drive the flow in the channel without transpiration. Data for the physics-informed neural network optimization is sampled using the Latin hypercube sampling method. The dataset, generated by direct numerical simulation, is divided into training and validation datasets. A deep neural network, consisting of multiple hidden layers, is utilized for constructing the surrogate model. The optimization process involves the use of Genetic Algorithms to search for acceptable local optimal values. The integration of GAs with the surrogate model involves several steps. Numerical experiments are conducted to validate the effectiveness of the PINN-based surrogate model approach. The results demonstrate an average acceptable error when comparing the test dataset with the predictions of the PINN surrogate model. Furthermore, the effectiveness of the proposed approach is demonstrated through a comparison between the results obtained from direct numerical simulation (DNS) and the predictions generated by the surrogate model. This comparative analysis serves to validate the accuracy and reliability of the surrogate model in capturing the key characteristics and behaviors of the flow control system.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Sun, G., Wang, S.: A review of the artificial neural network surrogate modeling in aerodynamic design. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering. 233(16), 5863–5872 (2019)
Sun, L., Wang, J.X.: Physics-constrained bayesian neural network for fluid flow reconstruction with sparse and noisy data. Theoretical Appl. Mech. Lett. 1, 10(3), 161–169 (2020)
Zhu, Q., Liu, Z., Yan, J.: Machine learning for metal additive manufacturing: predicting temperature and melt pool fluid dynamics using physics-informed neural networks. Comput. Mech.. Mech. 67, 619–635 (2021)
Forster, M., Feldman, J., Lyes, P., Johns, J., Warsop, C.: Surrogate modelling of active flow control. In: AIAA SCITECH 2023 Forum p. 2314 (2023)
Yondo, R., Bobrowski, K., Andrés, E., Valero, E.: A review of surrogate modeling techniques for aerodynamic analysis and optimization: current limitations and future challenges in industry. Advances in evolutionary and deterministic methods for design, optimization and control in engineering and sciences, pp. 19–33 (2019)
Vavalle, A., Qin, N.: Iterative response surface based optimization scheme for transonic airfoil design. J. Aircr.Aircr. 44(2), 365–376 (2007)
Sóbester, A., Leary, S.J., Keane, A.J.: On the design of optimization strategies based on global response surface approximation models. J. Global Optim.Optim. 33, 31–59 (2005)
Karmy, J.P., Maldonado, S.: Hierarchical time series forecasting via support vector regression in the European travel retail industry. Expert Syst. Appl. 137, 59–73 (2019)
Yun, Y., Yoon, M., Nakayama, H.: Multi-objective optimization based on meta-modeling by using support vector regression. Optim. Eng.. Eng. 10, 167–181 (2009)
Herzog, S., Tetzlaff, C., Wörgötter, F.: Evolving artificial neural networks with feedback. Neural Netw.Netw. 123, 153–162 (2020)
Booth, K., Bandler, J.: Space mapping for codesigned magnetics: optimization techniques for high-fidelity multidomain design specifications. IEEE Power Electronics Magazine 7(2), 47–52 (2020)
Bandler, J.W., Biernacki, R.M., Chen, S.H., Grobelny, P.A., Hemmers, R.H.: Space mapping technique for electromagnetic optimization. IEEE Trans. Microw. Theory Tech.Microw. Theory Tech. 42(12), 2536–2544 (1994)
Wang, Q., Moin, P., Iaccarino, G.: A rational interpolation scheme with superpolynomial rate of convergence. SIAM J. Numer. Anal.Numer. Anal. 47(6), 4073–4097 (2010)
Migliorati, G.: Multivariate approximation of functions on irregular domains by weighted least-squares methods. IMA J. Numer. Anal.Numer. Anal. 41(2), 1293–1317 (2021)
Ghauch, Z.G., Aitharaju, V., Rodgers, W.R., Pasupuleti, P., Dereims, A., Ghanem, R.G.: Integrated stochastic analysis of fiber composites manufacturing using adapted polynomial chaos expansions. Compos. A Appl. Sci. Manuf. 118, 179–193 (2019)
Novak, L., Novak, D.: Polynomial chaos expansion for surrogate modelling: theory and software. Beton-und Stahlbetonbau 113, 27–32 (2018)
Haghighat, E., Raissi, M., Moure, A., Gomez, H., Juanes, R.: A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics. Comput. Methods Appl. Mech. Eng.. Methods Appl. Mech. Eng. 379, 113741 (2021)
Lucor, D., Agrawal, A., Sergent, A.: Physics-aware deep neural networks for surrogate modeling of turbulent natural convection (2021). arXiv preprint arXiv:2103.03565
Sun, L., Gao, H., Pan, S., Wang, J.X.: Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data. Comput. Methods Appl. Mech. Eng.. Methods Appl. Mech. Eng. 361, 112732 (2020)
Batuwatta-Gamage, C.P., et al.: A physics-informed neural network-based surrogate framework to predict moisture concentration and shrinkage of a plant cell during drying. J. Food Eng. 332, 111137 (2022)
Acknowledgments
Supported in part by the Scientific and Technological Project of Henan Province (Grant No. 222102210056), The Key Scientific Project for the University of Henan Province (Grant No. 23A520003), and the Aeronautical Science Foundation of China (Grant No. 20200051042003).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Jiao, L., Zhang, D., Shang, J., Yang, G. (2024). Physics-Informed Neural Network Surrogate Modeling Approach of Active/Passive Flow Control for Drag Reduction. In: Sun, F., Meng, Q., Fu, Z., Fang, B. (eds) Cognitive Systems and Information Processing. ICCSIP 2023. Communications in Computer and Information Science, vol 1918. Springer, Singapore. https://doi.org/10.1007/978-981-99-8018-5_18
Download citation
DOI: https://doi.org/10.1007/978-981-99-8018-5_18
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-99-8017-8
Online ISBN: 978-981-99-8018-5
eBook Packages: Computer ScienceComputer Science (R0)