Abstract
Data Assimilation (DA) is a Bayesian inference that combines the state of a dynamical system with real data collected by instruments at a given time. The goal of DA is to improve the accuracy of the dynamic system making its result as real as possible. One of the most popular technique for DA is the Kalman Filter (KF). When the dynamic system refers to a real world application, the representation of the state of a physical system usually leads to a big data problem. For these problems, KF results computationally too expensive and mandates to use of reduced order modeling techniques. In this paper we proposed a new methodology we called Latent Assimilation (LA). It consists in performing the KF in the latent space obtained by an Autoencoder with non-linear encoder functions and non-linear decoder functions. In the latent space, the dynamic system is represented by a surrogate model built by a Recurrent Neural Network. In particular, an Long Short Term Memory (LSTM) network is used to train a function which emulates the dynamic system in the latent space. The data from the dynamic model and the real data coming from the instruments are both processed through the Autoencoder. We apply the methodology to a real test case and we show that the LA has a good performance both in accuracy and in efficiency.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Arcucci, R., Pain, C., Guo, Y.: Effective variational data assimilation in air-pollution prediction. Big Data Min. Anal. 1(4), 297–307 (2018)
Arcucci, R., Mottet, L., Pain, C., Guo, Y.: Optimal reduced space for variational data assimilation. J. Comput. Phys. 379, 51–69 (2019)
Arcucci, R., Zhu, J., Hu, S., Guo, Y.: Deep data assimilation: integrating deep learning with data assimilation. Appl. Sci. 11(3), 11–14 (2021). Multidisciplinary Digital Publishing Institute
Asch, M., Bocquet, M., Nodet, M.: Data Assimilation: Methods, Algorithms, and Applications. SIAM, Fundamentals of Algorithms, Philadelphia (2016)
Babovic, V., Keijzer, M., Bundzel, M.: From global to local modelling: a case study in error correction of deterministic models. In: Proceedings of Fourth International Conference on Hydroinformatics (2000)
Babovic, V., Caňizares, R., Jensen, H., Klinting, A.: Neural networks as routine for error updating of numerical models. J. Hydraul. Eng. 127(3), 181–193 (2001). American Society of Civil Engineers
Babovic, V., Fuhrman, D.: Data assimilation of local model error forecasts in a deterministic model. Int. J. Numer. Methods Fluids 39(10), 887–918 (2002). Wiley Online Library
Becker, P., Pandya, H., Gebhardt, G., Zhao, C., Taylor, J., Neumann, G.: Recurrent Kalman networks: factorized inference in high-dimensional deep feature spaces. arXiv preprint arXiv:1905.07357 (2019)
Boukabara, S., Krasnopolsky, V., Stewart, J., Maddy, E., Shahroudi, N., Hoffman, R.: Leveraging modern artificial intelligence for remote sensing and NWP: benefits and challenges. Bull. Am. Meteorol. Soc. 100(12), ES473–ES491 (2019)
Campos, R., Krasnopolsky, V., Alves, J., Penny, S.: Nonlinear wave ensemble averaging in the Gulf of Mexico using neural networks. J. Atmos. Oceanic Technol. 36(1), 113–127 (2019)
Cintra, R., Campos Velho, H.: Data assimilation by artificial neural networks for an atmospheric general circulation model. In: Advanced Applications for Artificial Neural Networks, p. 265. BoD-Books on Demand (2018)
Dozat, T.: Incorporating nesterov momentum into adam (2016)
Dueben, P., Bauer, P.: Challenges and design choices for global weather and climate models based on machine learning. Geosci. Model Dev. 11(10), 3999–4009 (2018). Copernicus GmbH
Funahashi, K., Nakamura, Y.: Approximation of dynamical systems by continuous time recurrent neural networks. Neural Netw. 6(6), 801–806 (1993). Elsevier
Gagne, D., McGovern, A., Haupt, S., Sobash, R., Williams, J., Xue, M.: Storm-based probabilistic hail forecasting with machine learning applied to convection-allowing ensembles. Weather Forecast. 32(5), 1819–1840 (2017)
Hannachi, A.: A primer for EOF analysis of climate data. Department of Meteorology University of Reading, pp. 1–33 (2004)
Hansen, P., Nagy, J., O’leary, D.: Deblurring Images: Matrices, Spectra, and Filtering, vol. 3. SIAM, Philadelphia (2006)
Kalman, R.: A new approach to linear filtering and prediction problems. J. Basic Eng. 82(1), 35–45 (1960). American Society of Mechanical Engineers
Loh, K., Omrani, P.S., van der Linden, R.: Deep learning and data assimilation for real-time production prediction in natural gas wells. arXiv preprint arXiv:1802.05141 (2018)
Rasp, S., Dueben, P., Scher, S., Weyn, J., Mouatadid, S., Thuerey, N.: WeatherBench: a benchmark dataset for data-driven weather forecasting. arXiv preprint arXiv:2002.00469 (2020)
Schäfer, A.M., Zimmermann, H.G.: Recurrent neural networks are universal approximators. In: Kollias, S.D., Stafylopatis, A., Duch, W., Oja, E. (eds.) ICANN 2006. LNCS, vol. 4131, pp. 632–640. Springer, Heidelberg (2006). https://doi.org/10.1007/11840817_66
Song, J., et al.: Natural ventilation in cities: the implications of fluid mechanics. Build. Res. Inform. 46(8), 809–828 (2018). Taylor & Francis
Watter, M., Springenberg, J., Boedecker, J., Riedmiller, M.: Embed to control: a locally linear latent dynamics model for control from raw images. In: Advances in Neural Information Processing Systems, pp. 2746–2754 (2015)
Wikle, C., Berliner, M.: A Bayesian tutorial for data assimilation. Phys. D Nonlinear Phenom. 230(1–2), 1–16 (2007). Elsevier
Zhu, J., Hu, S., Arcucci, R., Xu, C., Zhu, J., Guo, Y.: Model error correction in data assimilation by integrating neural networks. Big Data Min. Anal. 2(2), 83–91 (2019). TUP
Acknowledgements
This work is supported by the EPSRC Grand Challenge grant Managing Air for Green Inner Cities (MAGIC) EP/N010221/1, the EP/T003189/1 Health assessment across biological length scales for personal pollution exposure and its mitigation (INHALE), the EP/T000414/1 PREdictive Modelling with QuantIfication of UncERtainty for MultiphasE Systems (PREMIERE) and the Leonardo Centre for Sustainable Business at Imperial College London.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Amendola, M. et al. (2021). Data Assimilation in the Latent Space of a Convolutional Autoencoder. In: Paszynski, M., Kranzlmüller, D., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M. (eds) Computational Science – ICCS 2021. ICCS 2021. Lecture Notes in Computer Science(), vol 12746. Springer, Cham. https://doi.org/10.1007/978-3-030-77977-1_30
Download citation
DOI: https://doi.org/10.1007/978-3-030-77977-1_30
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-77976-4
Online ISBN: 978-3-030-77977-1
eBook Packages: Computer ScienceComputer Science (R0)