ConvPINNs: Integración de capas convolucionales a redes neurales de inferencia física
ConvPINNs integra capas convolucionales en Redes Neuronales de Inferencia Física (PINNs) para la resolución de ecuaciones diferenciales en la mecánica de fluidos. El trabajo explora dos enfoques distintos: uno que incluye la ecuación diferencial directamente en la función de pérdida con entradas de...
- Autores:
-
Gómez Barrera, Daniel Fernando
- Tipo de recurso:
- Trabajo de grado de pregrado
- Fecha de publicación:
- 2024
- Institución:
- Universidad de los Andes
- Repositorio:
- Séneca: repositorio Uniandes
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.uniandes.edu.co:1992/73874
- Acceso en línea:
- https://hdl.handle.net/1992/73874
- Palabra clave:
- Physics-informed neural networks
Partial differential equation solver
Pinns
Machine learning
Diffusion
Redes neurales de inferencia física
Solucionador de ecuaciones diferenciales parciales
Difusión
Ingeniería
- Rights
- openAccess
- License
- Attribution-NonCommercial-ShareAlike 4.0 International
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ConvPINNs: Integración de capas convolucionales a redes neurales de inferencia física |
| title |
ConvPINNs: Integración de capas convolucionales a redes neurales de inferencia física |
| spellingShingle |
ConvPINNs: Integración de capas convolucionales a redes neurales de inferencia física Physics-informed neural networks Partial differential equation solver Pinns Machine learning Diffusion Redes neurales de inferencia física Solucionador de ecuaciones diferenciales parciales Difusión Ingeniería |
| title_short |
ConvPINNs: Integración de capas convolucionales a redes neurales de inferencia física |
| title_full |
ConvPINNs: Integración de capas convolucionales a redes neurales de inferencia física |
| title_fullStr |
ConvPINNs: Integración de capas convolucionales a redes neurales de inferencia física |
| title_full_unstemmed |
ConvPINNs: Integración de capas convolucionales a redes neurales de inferencia física |
| title_sort |
ConvPINNs: Integración de capas convolucionales a redes neurales de inferencia física |
| dc.creator.fl_str_mv |
Gómez Barrera, Daniel Fernando |
| dc.contributor.advisor.none.fl_str_mv |
González Mancera, Andrés Leonardo |
| dc.contributor.author.none.fl_str_mv |
Gómez Barrera, Daniel Fernando |
| dc.subject.keyword.eng.fl_str_mv |
Physics-informed neural networks Partial differential equation solver Pinns Machine learning Diffusion |
| topic |
Physics-informed neural networks Partial differential equation solver Pinns Machine learning Diffusion Redes neurales de inferencia física Solucionador de ecuaciones diferenciales parciales Difusión Ingeniería |
| dc.subject.keyword.spa.fl_str_mv |
Redes neurales de inferencia física Solucionador de ecuaciones diferenciales parciales Difusión |
| dc.subject.themes.spa.fl_str_mv |
Ingeniería |
| description |
ConvPINNs integra capas convolucionales en Redes Neuronales de Inferencia Física (PINNs) para la resolución de ecuaciones diferenciales en la mecánica de fluidos. El trabajo explora dos enfoques distintos: uno que incluye la ecuación diferencial directamente en la función de pérdida con entradas de una grilla espaciotemporal y otro que opera con una entrada bidimensional de condiciones iniciales, sin considerar el tiempo como variable explícita. El propósito de este estudio es evaluar si la integración de redes convolucionales simples contribuyen a una mejora en la interpretación y en la capacidad predictiva de los modelos, en comparación con las PINNs convencionales que utilizan redes completamente conectadas (FCN). |
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2024-02-02T23:10:37Z |
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2024-02-01 |
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Trabajo de grado - Pregrado |
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Baydin, A. G., Pearlmutter, B. A., y Siskind, J. M. (2018). Automatic differentiation in machine learning: a survey. The Journal of Machine Learning Research, 18 , 1-43. Brunton, S. L., Noack, B. R., y Koumoutsakos, P. (2020, 1). Machine learning for fluid mechanics. https://doi.org/10.1146/annurev-fluid-010719-060214 , 52 , 477-508. Descargado de https://www.annualreviews.org/doi/abs/10.1146/annurev-fluid-010719-060214 doi: 10.1146/ANNUREV-FLUID-010719-060214 Cai, S., Mao, Z.,Wang, Z., Yin, M., y Karniadakis, G. E. (2021). Physics-informed neural networks (pinns) for fluid mechanics: A review. Acta Mechanica Sinica, ppb-ppb. Champion, K., Lusch, B., Kutz, J. N., y Brunton, S. L. (2019, 11). Data-driven discovery of coordinates and governing equations. Proceedings of the National Academy of Sciences of the United States of America, 116 , 22445-22451. Descargado de https://www.pnas.org/doi/abs/10.1073/pnas.1906995116 doi: 10.1073/PNAS.1906995116/SUPPL FILE/PNAS.1906995116.SAPP.PDF Chiu, P. H., Wong, J. C., Ooi, C., Dao, M. H., y Ong, Y. S. (2022, 5). Can-pinn: A fast physics-informed neural network based on coupled-automatic–numerical differentiation method. Computer Methods in Applied Mechanics and Engineering, 395 , 114909. doi: 10.1016/J.CMA.2022.114909 Cuomo, S., Schiano, V., Cola, D., Giampaolo, F., Rozza, G., Raissi, M., y Piccialli, F. (2022, 7). Scientific machine learning through physics–informed neural networks: Where we are and what’s next. Journal of Scientific Computing 2022 92:3 , 92 , 1-62. Descargado de https://link.springer.com/article/10.1007/s10915-022-01939-z doi: 10.1007/S10915-022-01939-Z Dumoulin, V., y Visin, F. (2016, 3). A guide to convolution arithmetic for deep learning. Descargado de https://arxiv.org/abs/1603.07285v2 doi: 10.48550/arxiv.1603.07285 Fang, Z. (2022, 10). A high-efficient hybrid physics-informed neural networks based on convolutional neural network. IEEE Transactions on Neural Networks and Learning Systems, 33 , 5514-5526. doi: 10.1109/TNNLS.2021.3070878 Gao, H., Sun, L., yWang, J. X. (2020, 4). Phygeonet: Physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state pdes on irregular domain. Journal of Computational Physics, 428 . Descargado de https://arxiv.org/abs/2004.13145v2 doi: 10.1016/j.jcp.2020.110079 Kolmogorov, A. N. (1991). The local structure of turbulence in incompressible viscous fluid for very large reynolds numbers. Proceedings: Mathematical and Physical Sciences, 434 , 9-13. Descargado de http://www.jstor.org.ezproxy.uniandes.edu.co/stable/51980 Leiteritz, R., y Uger, D. P. (2021, 12). How to avoid trivial solutions in physics-informed neural networks. Descargado de https://arxiv.org/abs/2112.05620v1 Long, J., Shelhamer, E., y Darrell, T. (2015). Fully convolutional networks for semantic segmentation. En (p. 3431-3440). Descargado de http://arxiv.org/abs/1411.4038 doi: 10.1109/CVPR.2015.7298965 Milano, M., y Koumoutsakos, P. (2002, 10). Neural network modeling for near wall turbulent flow. Journal of Computational Physics, 182 , 1-26. doi: 10.1006/JCPH.2002.7146 Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., Facebook, Z. D., . . . Lerer, A. (2017). Automatic differentiation in pytorch.. Raissi, M., Perdikaris, P., y Karniadakis, G. E. (2017, 11). Physics informed deep learning: Data-driven solutions of nonlinear partial differential equations. Descargado de https://arxiv.org/abs/1711.10561v1 doi: 10.48550/arxiv.1711.10561 Ren, P., Rao, C., Liu, Y., Wang, J., y Sun, H. (2021, 6). Phycrnet: Physics-informed convolutionalrecurrent network for solving spatiotemporal pdes. doi: 10.1016/j.cma.2021.114399 Shi, P., Zeng, Z., y Liang, T. (2022, 1). Physics-informed convnet: Learning physical field from a shallow neural network. Descargado de https://arxiv.org/abs/2201.10967v2 doi: 10.48550/arxiv.2201.10967 Waite, E. (2018). Pytorch autograd explained - in-depth tutorial. Descargado de https://www.youtube.com/watch?v=MswxJw-8PvE Zhou, D. X. (2018, 5). Universality of deep convolutional neural networks. Applied and Computational Harmonic Analysis, 48 , 787-794. Descargado de https://arxiv.org/abs/1805.10769v2 doi: 10.48550/arxiv.1805.10769 |
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Al consultar y hacer uso de este recurso, está aceptando las condiciones de uso establecidas por los autoresAttribution-NonCommercial-ShareAlike 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2González Mancera, Andrés LeonardoGómez Barrera, Daniel Fernando2024-02-02T23:10:37Z2024-02-02T23:10:37Z2024-02-01https://hdl.handle.net/1992/73874instname:Universidad de los Andesreponame:Repositorio Institucional Sénecarepourl:https://repositorio.uniandes.edu.co/ConvPINNs integra capas convolucionales en Redes Neuronales de Inferencia Física (PINNs) para la resolución de ecuaciones diferenciales en la mecánica de fluidos. El trabajo explora dos enfoques distintos: uno que incluye la ecuación diferencial directamente en la función de pérdida con entradas de una grilla espaciotemporal y otro que opera con una entrada bidimensional de condiciones iniciales, sin considerar el tiempo como variable explícita. El propósito de este estudio es evaluar si la integración de redes convolucionales simples contribuyen a una mejora en la interpretación y en la capacidad predictiva de los modelos, en comparación con las PINNs convencionales que utilizan redes completamente conectadas (FCN).ConvPINNs integrates convolutional layers into Physics-Informed Neural Networks (PINNs) for solving differential equations in fluid mechanics. The work explores two distinct approaches: one that incorporates the differential equation directly into the loss function with inputs from a spatiotemporal grid and another that operates with a two-dimensional input of initial conditions, without considering time as an explicit variable. The purpose of this study is to assess whether the integration of simple convolutional networks contributes to an improvement in interpretability and predictive accuracy of the models, compared to conventional PINNs that utilize fully connected networks (FCN).Ingeniero MecánicoPregrado39 páginasapplication/pdfspaUniversidad de los AndesIngeniería MecánicaFacultad de IngenieríaDepartamento de Ingeniería MecánicaConvPINNs: Integración de capas convolucionales a redes neurales de inferencia físicaTrabajo de grado - Pregradoinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_7a1fTexthttp://purl.org/redcol/resource_type/TPPhysics-informed neural networksPartial differential equation solverPinnsMachine learningDiffusionRedes neurales de inferencia físicaSolucionador de ecuaciones diferenciales parcialesDifusiónIngenieríaBaydin, A. G., Pearlmutter, B. A., y Siskind, J. M. (2018). Automatic differentiation in machine learning: a survey. The Journal of Machine Learning Research, 18 , 1-43.Brunton, S. L., Noack, B. R., y Koumoutsakos, P. (2020, 1). Machine learning for fluid mechanics. https://doi.org/10.1146/annurev-fluid-010719-060214 , 52 , 477-508. Descargado de https://www.annualreviews.org/doi/abs/10.1146/annurev-fluid-010719-060214 doi: 10.1146/ANNUREV-FLUID-010719-060214Cai, S., Mao, Z.,Wang, Z., Yin, M., y Karniadakis, G. E. (2021). Physics-informed neural networks (pinns) for fluid mechanics: A review. Acta Mechanica Sinica, ppb-ppb.Champion, K., Lusch, B., Kutz, J. N., y Brunton, S. L. (2019, 11). Data-driven discovery of coordinates and governing equations. Proceedings of the National Academy of Sciences of the United States of America, 116 , 22445-22451. Descargado de https://www.pnas.org/doi/abs/10.1073/pnas.1906995116 doi: 10.1073/PNAS.1906995116/SUPPL FILE/PNAS.1906995116.SAPP.PDFChiu, P. H., Wong, J. C., Ooi, C., Dao, M. H., y Ong, Y. S. (2022, 5). Can-pinn: A fast physics-informed neural network based on coupled-automatic–numerical differentiation method. Computer Methods in Applied Mechanics and Engineering, 395 , 114909. doi: 10.1016/J.CMA.2022.114909Cuomo, S., Schiano, V., Cola, D., Giampaolo, F., Rozza, G., Raissi, M., y Piccialli, F. (2022, 7). Scientific machine learning through physics–informed neural networks: Where we are and what’s next. Journal of Scientific Computing 2022 92:3 , 92 , 1-62. Descargado de https://link.springer.com/article/10.1007/s10915-022-01939-z doi: 10.1007/S10915-022-01939-ZDumoulin, V., y Visin, F. (2016, 3). A guide to convolution arithmetic for deep learning. Descargado de https://arxiv.org/abs/1603.07285v2 doi: 10.48550/arxiv.1603.07285Fang, Z. (2022, 10). A high-efficient hybrid physics-informed neural networks based on convolutional neural network. IEEE Transactions on Neural Networks and Learning Systems, 33 , 5514-5526. doi: 10.1109/TNNLS.2021.3070878Gao, H., Sun, L., yWang, J. X. (2020, 4). Phygeonet: Physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state pdes on irregular domain. Journal of Computational Physics, 428 . Descargado de https://arxiv.org/abs/2004.13145v2 doi: 10.1016/j.jcp.2020.110079Kolmogorov, A. N. (1991). The local structure of turbulence in incompressible viscous fluid for very large reynolds numbers. Proceedings: Mathematical and Physical Sciences, 434 , 9-13. Descargado de http://www.jstor.org.ezproxy.uniandes.edu.co/stable/51980Leiteritz, R., y Uger, D. P. (2021, 12). How to avoid trivial solutions in physics-informed neural networks. Descargado de https://arxiv.org/abs/2112.05620v1Long, J., Shelhamer, E., y Darrell, T. (2015). Fully convolutional networks for semantic segmentation. En (p. 3431-3440). Descargado de http://arxiv.org/abs/1411.4038 doi: 10.1109/CVPR.2015.7298965Milano, M., y Koumoutsakos, P. (2002, 10). Neural network modeling for near wall turbulent flow. Journal of Computational Physics, 182 , 1-26. doi: 10.1006/JCPH.2002.7146Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., Facebook, Z. D., . . . Lerer, A. (2017). Automatic differentiation in pytorch..Raissi, M., Perdikaris, P., y Karniadakis, G. E. (2017, 11). Physics informed deep learning: Data-driven solutions of nonlinear partial differential equations. Descargado de https://arxiv.org/abs/1711.10561v1 doi: 10.48550/arxiv.1711.10561Ren, P., Rao, C., Liu, Y., Wang, J., y Sun, H. (2021, 6). Phycrnet: Physics-informed convolutionalrecurrent network for solving spatiotemporal pdes. doi: 10.1016/j.cma.2021.114399Shi, P., Zeng, Z., y Liang, T. (2022, 1). Physics-informed convnet: Learning physical field from a shallow neural network. Descargado de https://arxiv.org/abs/2201.10967v2 doi: 10.48550/arxiv.2201.10967Waite, E. (2018). Pytorch autograd explained - in-depth tutorial. Descargado de https://www.youtube.com/watch?v=MswxJw-8PvEZhou, D. X. (2018, 5). Universality of deep convolutional neural networks. Applied and Computational Harmonic Analysis, 48 , 787-794. 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