Latent Space Exploration of Particle Discharge Using Autoencoders Trained on Discrete Element Method Simulations
DOI:
https://doi.org/10.70567/mc.v42.ocsid8469Keywords:
Variational Autoencoder, Dimensionality Reduction, Granular Flows, PCA, Latent RepresentationsAbstract
In recent years, variational autoencoders (VAEs) have established themselves as a powerful tool for learning compact and continuous representations of complex systems. In this work, a convolutional VAE is applied to the task of predicting the temporal evolution in a granular flow system simulated by the discrete element method (DEM). The model is trained to take as input two consecutive images from the simulation and generate as output the images of the following time steps. Subsequently, the resulting latent space is analyzed using Principal Component Analysis (PCA), with the aim of evaluating whether the latent representations capture relevant information about the system’s state. The results show that the model is capable of organizing the data into differentiated regions with temporal continuity, which constitutes favorable evidence that the VAE has learned useful state variables to describe the system.
References
Baldi P. y Hornik K. Neural networks and principal component analysis: Learning from examples
without local minima. Neural Networks, 2(1):53–58, 1989.
Berkooz G., Holmes P., y Lumley J.L. The proper orthogonal decomposition in the analysis of
turbulent flows. Annual Review of Fluid Mechanics, 25(1):539–575, 1993.
Bertone S., Puccini G., Monier E., y Jappert S. Simulación de flujos de sólidos a granel en tolvas utilizando modelos de elementos discretos. XII Congreso Argentino de Mecánica Computacional Mecom 2018, páginas 1–10, 2018.
Bertone S.E., Puccini G.D., Bonetti C., Denardi M., y Bianchotti J. Impacto de las vibracionesmecánicas en la descarga de sólidos a granel en una tolva bidimensional: un análisis basado en modelos de elementos discretos. Mecánica Computacional, 40(36):1285–1292, 2023.
Bertone S.E., Puccini G.D., Bonetti C.A., Denardi M., y Bianchotti J.D. Reducción de la dimensionalidad de un sistema de partículas en movimiento utilizando redes neuronales convolucionales. Mecánica Computacional, 41(19):1023–1031, 2024.
Bonheme L. y Grzes M. How do variational autoencoders learn? insights from representational similarity. arXiv preprint arXiv:2205.08399, 2022.
Brunton S.L., Proctor J.L., y Kutz J.N. Proceedings of the national academy of sciences. Proceedings of the National Academy of Sciences, 113(14):3932–3939, 2016. https://doi.org/10.1073/pnas.1517792113.
Champion K., Lusch B., Kutz J.N., y Brunton S.L. Proceedings of the national academy of sciences. Proceedings of the National Academy of Sciences, 116(45):22445–22454, 2019. https://doi.org/10.1073/pnas.1911627116.
Chen B., Huang K., Raghupathi S., Chandratreya I., Du Q., y Lipson H. Discovering state variables hidden in experimental data. 2021. https://doi.org/10.48550/arXiv.2112.10755.
Cundall P. y Strack O. A discrete numerical model for granular assemblies. Geotechnique, 29(1):47–65, 1979.
Goodfellow I., Bengio Y., Courville A., y Bengio Y. Deep Learning, volumen 1. MIT Press, Cambridge, 2016.
Goroshin R., Bruna J., Tompson J., Eigen D., y LeCun Y. Unsupervised learning of spatiotemporally coherent metrics. En Proceedings of the IEEE international conference on computer vision, páginas 4086–4093. 2015.
Gregor K., Danihelka I., Graves A., Rezende D., y Wierstra D. Draw: A recurrent neural network for image generation. En International conference on machine learning, páginas 1462– 1471. PMLR, 2015.
Holmes P.J., Lumley J.L., Berkooz G., y Rowley C.W. Turbulence, coherent structures, dynamical systems and symmetry. Cambridge Monographs in Mechanics. Cambridge University Press, Cambridge, England, 2nd edición, 2012.
Kingma D.P., Rezende D.J., Mohamed S., y Welling M. Semi-supervised learning with deep generative models. Advances in neural information processing systems, 27, 2014.
Kloss C., Goniva C., Hager A., Amberger S., y Pirker S. Models, algorithms and validation for opensource DEM and CFD-DEM. Progress in Computational Fluid Dynamics, An Int. J., 12(2/3):140–152, 2012.
Pearson K. On lines and planes of closest fit to systems of points in space. Philosophical Magazine, 2(7-12):559–572, 1901.
Taira K., Brunton S.L., Dawson S.T.M., Rowley C.W., Colonius T., McKeon B.J., Schmidt O.T., Gordeyev S., Theofilis V., y Ukeiley L.S. Modal analysis of fluid flows: An overview. AIAA Journal, 55(12):4013–4041, 2017.
Udrescu S.M. y Tegmark M. Science advances. Science Advances, 6(23):eaay2631, 2020.https://doi.org/10.1126/sciadv.aay2631.
Walker J., Razavi A., y Oord A.v.d. Predicting video with vqvae. arXiv preprint ar-Xiv:2103.01950, 2021.
Zhu H., Zhou Z., Yang R., y Yu A. Discrete particle simulation of particulate systems: theoretical developments. Chemical Engineering Science, 62(13):3378–3396, 2007.
Zhu H., Zhou Z., Yang R., y Yu A. Discrete particle simulation of particulate systems: a review of major applications and findings. Chemical Engineering Science, 63(23):5728–5770, 2008.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Argentine Association for Computational Mechanics
This work is licensed under a Creative Commons Attribution 4.0 International License.
This publication is open access diamond, with no cost to authors or readers.
Only those papers that have been accepted for publication and have been presented at the AMCA congress will be published.
