EGU2020-20845, updated on 04 Jun 2020
https://doi.org/10.5194/egusphere-egu2020-20845
EGU General Assembly 2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Learning Lyapunov stable Dynamical Embeddings of Geophysical Dynamics

Said Ouala1, Lucas Drumetz1, Bertrand Chapron2, Ananda Pascual3, Fabrice Collard4, Lucile Gaultier4, and Ronan Fablet1
Said Ouala et al.
  • 1IMT Atlantique, Lab STICC, Signal et communications, France (said.ouala@imt-atlantique.fr)
  • 2Ifremer, LOPS, Brest, France
  • 3IMEDEA, UIB-CSIC, Esporles, Spain
  • 4ODL, Brest, France

Within the geosciences community, data-driven techniques have encountered a great success in the last few years. This is principally due to the success of machine learning techniques in several image and signal processing domains. However, when considering the data-driven simulation of ocean and atmospheric fields, the application of these methods is still an extremely challenging task due to the fact that the underlying dynamics usually depend on several complex hidden variables, which makes the learning and simulation process much more challenging.

In this work, we aim to extract Ordinary Differential Equations (ODE) from partial observations of a system. We propose a novel neural network architecture guided by physical and mathematical considerations of the underlying dynamics. Specifically, our architecture is able to simulate the dynamics of the system from a single initial condition even if the initial condition does not lie in the attractor spanned by the training data. We show on different case studies the effectiveness of the proposed framework both in capturing long term asymptotic patterns of the dynamics of the system and in addressing data assimilation issues which relates to the short term forecasting performance of our model.

How to cite: Ouala, S., Drumetz, L., Chapron, B., Pascual, A., Collard, F., Gaultier, L., and Fablet, R.: Learning Lyapunov stable Dynamical Embeddings of Geophysical Dynamics, EGU General Assembly 2020, Online, 4–8 May 2020, https://doi.org/10.5194/egusphere-egu2020-20845, 2020

Comments on the presentation

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Presentation version 2 – uploaded on 06 May 2020
I removed the "no show" slides, since they were still visible in the first version.
  • CC1: Comment on EGU2020-20845, Paul Pukite, 06 May 2020

    How can one extract a description of the differential equation when the forcing is unknown?  In other words, when the forced response overrides the natural response, the character of the diffEq is not as important.  Consider a conventional  tidal response. That is essentially a completely forced response even though differential equations (N-S fluid dynamics eqns) do play a role.

  • AC1: Comment on EGU2020-20845, Said OUALA, 06 May 2020

    Dear sir, 

    I believe that when the forcing overrides the natural response of a system, the extracted model naturally (due to the learning criterion) relates the forcing signature to the dynamics and thus, approximates the forced system with a non-foreced one. This approximation may be crude but one can add a learnable forcing signatures (similarly to what we did with the learnable embedding) to find an approximate forced system. However, without any prior knowledge of either the dynamics or the forcing, the latter approximation will not be quite informative since forcing signatures will mixed with the natural dynamics of the system.

    • CC2: Reply to AC1, Paul Pukite, 06 May 2020

      That's true. Both the initial conditions (as you say) and the running boundary values as either ongoing temporal forcing or spatial boundary conditions play a role. Thank you.

Presentation version 1 – uploaded on 04 May 2020 , no comments