Madrid Wagner, Martín (2024) Aplicación de técnicas de reducción dimensional en el modelado de flujos inestables / Application of dimensionality reducction techniques in medeling unstable flows. Proyecto Integrador Ingeniería Nuclear, Universidad Nacional de Cuyo, Instituto Balseiro.
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Resumen en español
La dinámica de fluidos computacional (CFD) se caracteriza por producir datos espaciotemporales de alta dimensión. Por lo tanto, identificar un conjunto óptimo de coordenadas para representar los datos en un subespacio latente de baja dimensión es un primer paso hacia el desarrollo de modelos de orden reducido. El abordaje tradicional es mediante el Análisis de Componentes Principales (PCA), que da una aproximación lineal óptima. Sin embargo, en general los flujos son complejos e inherentemente no-lineales, lo cual limita la capacidad de representación en baja dimensión del PCA. En consecuencia, recientemente se han comenzado a aplicar en el campo del CFD algoritmos de reducción de dimensionalidad (RD) no-lineales, originalmente desarrollados en el área del aprendizaje automático. En este contexto, en el presente trabajo se busca implementar y comparar diferentes métodos de RD, lineal y no-lineales, en un problema canónico de flujo inestable: el flujo alrededor de un cilindro inmerso en un flujo uniforme. Para ello, en primer lugar se genera una base de datos a partir de simulaciones numéricas directas (DNS) con el software Xcompact3d a diferentes números de Reynolds. Luego se implementan las distintas técnicas de RD. Las mismas incluyen el estándar lineal PCA, que actúa como referencia para comparar el rendimiento de los métodos no-lineales implementados: Kernel PCA (KPCA), Locally Linear Embedding (LLE), Isometric Mapping (Isomap) y autoencoders (AE). En este marco, se comparan cuantitativamente las calidades de reconstrucción de estos métodos. Las técnicas no-lineales presentan mejores resultados en la reducción espacial, pero no superan al PCA en la reducción temporal. Sin embargo, la disposición temporal de los datos permite extraer modos espaciales visualizables que resaltan las principales estructuras características del flujo, facilitando la comparación cualitativa de los métodos.
Resumen en inglés
Computational fluid dynamics (CFD) is characterized by producing high-dimensional spatiotemporal data. Therefore, identifying an optimal set of coordinates to represent the data in a low-dimensional latent subspace is a first step toward the development of reduced-order models. The traditional approach is Principal Component Analysis (PCA), which provides an optimal linear approximation. However, fluid flows are generally complex and inherently nonlinear, limiting the low-dimensional representation capability of PCA. Consequently, non-linear dimensionality reduction (DR) algorithms, originally developed in the field of machine learning, have recently begun to be applied in the field of CFD. In this context, this work aims to implement and compare different linear and nonlinear DR methods over a canonical unsteady flow problem: the flow around a cylinder immersed in a uniform stream. To this end, a database is generated from direct numerical simulations (DNS) using the Xcompact3d software at different Reynolds numbers. The DR techniques studied include the standard linear PCA, which serves as a reference for comparing the performance of the implemented nonlinear methods: Kernel PCA (KPCA), Locally Linear Embedding (LLE), Isometric Mapping (Isomap), and autoencoders (AE). The reconstruction quality of these methods is quantitatively compared. Nonlinear techniques show better results in spatial reduction,but do not outperform PCA in temporal reduction. However, the temporal arrangement of the data allows for the extraction of visualizable spatial modes that highlight the main characteristic structures of the flow, facilitating the qualitative comparison of the methods.
| Tipo de objeto: | Tesis (Proyecto Integrador Ingeniería Nuclear) |
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| Palabras Clave: | Computational fluid dynamics; Dinámica de fluidos computacional; [Unsteady flow modeling; Modelado de flujo inestable; Dimensionality reduction; Reducción dimensional] |
| Referencias: | [1] Taira, K., Brunton, S. L., Dawson, S. T. M., Rowley, C. W., Colonius, T., McKeon, B. J., et al. Modal analysis of fluid flows: An overview, 2017. 1 [2] Csala, H., Dawson, S., Arzani, A. Comparing different nonlinear dimensionality reduction techniques for data-driven unsteady fluid flow modeling. Physics of Fluids, 34 (11), 2022. 2, 66, 72, 73 [3] Wang, Z., Zhang, G., Xing, X., Xu, X., Sun, T. Comparison of dimensionality reduction techniques for multi-variable spatiotemporal flow fields. Ocean Engineering, 291, 116421, 2024. 2 [4] Ahmed, S. E., Pawar, S., San, O., Rasheed, A., Iliescu, T., Noack, B. R. On closures for reduced order models—a spectrum of first-principle to machine-learned avenues. Physics of Fluids, 33 (9), 2021. 2 [5] Rowley, C. W., Colonius, T., Murray, R. M. Model reduction for compressible flows using pod and galerkin projection. Physica D: Nonlinear Phenomena, 189 (1), 115–129, 2004. URL https://www.sciencedirect.com/science/article/pii/S0167278903003841. 2 [6] Geron, A. Hands-on machine learning with Scikit-Learn, Keras, and TensorFlow..O’Reilly Media, Inc.”, 2022. ix, ix, ix, x, x, 3, 4, 25, 33 [7] Ghojogh, B., Crowley, M., Karray, F., Ghodsi, A. Elements of dimensionality reduction and manifold learning. Springer Nature, 2023. xi, 4, 34, 36 [8] Kundu, P. K., Cohen, I. M., Dowling, D. R. Fluid mechanics. Academic press, 2015. 4, 12 [9] Sato, M., Kobayashi, T. A fundamental study of the flow past a circular cylinder using abaqus/cfd. En: 2012 SIMULIA Community Conference. 2012. ix, 5, 6 [10] Hughes, W. F., Brighton, J. A. Fluid dynamics. McGraw-Hill, 1999. 679 [11] Bartholomew, P., Deskos, G., Frantz, R. A., Schuch, F. N., Lamballais, E., Laizet, S. Xcompact3d: An open-source framework for solving turbulence problems on a cartesian mesh. SoftwareX, 12, 100550, 2020. 9, 10 [12] Pope, S. B. Turbulent flows. Measurement Science and Technology, 12 (11), 2020–2021, 2001. 9, 12 [13] Li, N., Laizet, S. 2decomp & fft-a highly scalable 2d decomposition library and fft interface. En: Cray user group 2010 conference, págs. 1–13. 2010. 10 [14] Machaca Abregu, W. I., Dari, E. A., Teruel, F. E. Conjugate heat transfer in spatial laminar-turbulent transitional channel flow. International Communications in Heat and Mass Transfer, 154, 107430, 2024. URL https://www.sciencedirect.com/science/article/pii/S0735193324001921. 10 [15] Machaca Abregu, W. I., Dari, E. A., Teruel, F. E. Dns of heat transfer in a plane channel flow with spatial transition. International Journal of Heat and Mass Transfer, 209, 124110, 2023. URL https://www.sciencedirect.com/science/article/pii/S0017931023002636. 10 [16] Lele, S. K. Compact finite difference schemes with spectral-like resolution. Journal of Computational Physics, 103 (1), 16–42, 1992. URL https://www.sciencedirect.com/science/article/pii/002199919290324R. 11 [17] Chorin, A. J. Numerical solution of the navier-stokes equations. Mathematics of computation, 22 (104), 745–762, 1968. 11 [18] Kader, B., Yaglom, A. Heat and mass transfer laws for fully turbulent wall flows. International Journal of Heat and Mass Transfer, 15 (12), 2329–2351, 1972. 12 [19] Schafer, M., Turek, S., Durst, F., Krause, E., Rannacher, R. Benchmark computations of laminar flow around a cylinder. Springer, 1996. 12 [20] Lee, M., Moser, R. D. Direct numerical simulation of turbulent channel flow up to Reτ ≈ 5200. Journal of Fluid Mechanics, 774, 395–415, 2015. ix, 12, 13 [21] Vreman, A., Kuerten, J. G. Comparison of direct numerical simulation databases of turbulent channel flow at reτ= 180. Physics of Fluids, 26 (1), 2014. ix, 13 [22] Mittal, R., Balachandar, S., et al. On the inclusion of three-dimensional effects in simulations of two-dimensional bluff-body wake flows. En: ASME fluids engineering division summer meeting, págs. 1–6. Citeseer, 1997. ix, 12, 14 [23] Brunton, S. L., Kutz, J. N. Data-driven science and engineering: Machine learning, dynamical systems, and control. Cambridge University Press, 2022. 21, 23, 24 [24] Scholkopf, B., Smola, A., Muller, K.-R. Nonlinear component analysis as a kernel eigenvalue problem. Neural computation, 10 (5), 1299–1319, 1998. x, 28, 30 [25] Aizerman, A. Theoretical foundations of the potential function method in pattern recognition learning. Automation and remote control, 25, 821–837, 1964. 31 [26] Honeine, P., Richard, C. Preimage problem in kernel-based machine learning. IEEE Signal Processing Magazine, 28 (2), 77–88, 2011. 32 [27] Bakır, G. H., Weston, J., Scholkopf, B. Learning to find pre-images. Advances in neural information processing systems, 16, 449–456, 2004. 32 [28] Murphy, K. P. Machine learning: a probabilistic perspective. MIT press, 2012. 32 [29] Roweis, S. T., Saul, L. K. Nonlinear dimensionality reduction by locally linear embedding. science, 290 (5500), 2323–2326, 2000. 33 [30] Saul, L. K., Roweis, S. T. An introduction to locally linear embedding. unpublished. Available at: http://www.cs.toronto.edu/˜roweis/lle/publications.html, 2000. 33 [31] Tenenbaum, J. B., Silva, V. d., Langford, J. C. A global geometric framework for nonlinear dimensionality reduction. science, 290 (5500), 2319–2323, 2000. xi, 38, 39 [32] Torgerson, W. S. Multidimensional scaling: I. theory and method. Psychometrika, 17 (4), 401–419, 1952. 38 [33] Cormen, T. H., Leiserson, C. E., Rivest, R. L., Stein, C. Introduction to algorithms. MIT press, 2022. 39 [34] Plaut, E. From principal subspaces to principal components with linear autoencoders, 2018. 42, 72 [35] Prince, S. J. Understanding Deep Learning. MIT press, 2023. xi, xi, 42, 43, 44 [36] Kingma, D. P., Ba, J. Adam: A method for stochastic optimization, 2014. 46, 47 [37] Brunton, S. L., Noack, B. R., Koumoutsakos, P. Machine learning for fluid mechanics. Annual review of fluid mechanics, 52, 477–508, 2020. xi, 48 [38] Gautier, R., Laizet, S., Lamballais, E. A dns study of jet control with microjets using an immersed boundary method. International Journal of Computational Fluid Dynamics, 28 (6-10), 393–410, 2014. 52 [39] Agostini, L. Exploration and prediction of fluid dynamical systems using autoencoder technology. Physics of Fluids, 32 (6), 2020. 73 [40] Cheng, M., Fang, F., Pain, C., Navon, I. An advanced hybrid deep adversarial autoencoder for parameterized nonlinear fluid flow modelling. Computer Methods in Applied Mechanics and Engineering, 372, 113375, 2020. 73 [41] Belkin, M., Niyogi, P. Laplacian Eigenmaps for Dimensionality Reduction and Data Representation. Neural Computation, 15 (6), 1373–1396, 06 2003. URL https://doi.org/10.1162/089976603321780317. 73 [42] Donoho, D. L., Grimes, C. Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data. Proceedings of the National Academy of Sciences, 100 (10), 5591–5596, 2003. 73 [43] Zhao, X., Zhang, S. Facial expression recognition using local binary patterns and discriminant kernel locally linear embedding. EURASIP journal on Advances in signal processing, 2012, 1–9, 2012. 73 [44] Wang, Z., Zhang, G., Sun, T., Shi, C., Zhou, B. Data-driven methods for lowdimensional representation and state identification for the spatiotemporal structure of cavitation flow fields. Physics of Fluids, 35 (3), 2023. 73 |
| Materias: | Ingeniería |
| Divisiones: | Gcia. de área de Aplicaciones de la tecnología nuclear > Gcia. de Investigación aplicada > Mecánica computacional |
| Código ID: | 1279 |
| Depositado Por: | Tamara Cárcamo |
| Depositado En: | 12 Sep 2024 10:24 |
| Última Modificación: | 12 Sep 2024 10:24 |
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