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Variational Deep Learning for the Identification and Reconstruction of Chaotic and Stochastic Dynamical Systems from Noisy and Partial Observations

Duong Nguyen 1 Said Ouala 1 Lucas Drumetz 1 Ronan Fablet 1, 2
2 Lab-STICC_IMTA_CID_TOMS
Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
Abstract : The data-driven recovery of the unknown governing equations of dynamical systems has recently received an increasing interest. However, the identification of governing equations remains challenging when dealing with noisy and partial observations. Here, we address this challenge and investigate variational deep learning schemes. Within the proposed framework, we jointly learn an inference model to reconstruct the true states of the system and the governing laws of these states from series of noisy and partial data. In doing so, this framework bridges classical data assimilation and state-of-the-art machine learning techniques. We also demonstrate that it generalises state-of-the-art methods. Importantly, both the inference model and the governing model embed stochastic components to account for stochastic variabilities, model errors, and reconstruction uncertainties. Various experiments on chaotic and stochastic dynamical systems support the relevance of our scheme w.r.t. state-of-the-art approaches.
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https://hal.archives-ouvertes.fr/hal-02931101
Contributor : Duong Nguyen <>
Submitted on : Tuesday, February 16, 2021 - 6:14:25 PM
Last modification on : Wednesday, April 21, 2021 - 3:26:58 PM

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  • HAL Id : hal-02931101, version 7

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Duong Nguyen, Said Ouala, Lucas Drumetz, Ronan Fablet. Variational Deep Learning for the Identification and Reconstruction of Chaotic and Stochastic Dynamical Systems from Noisy and Partial Observations. 2021. ⟨hal-02931101v7⟩

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