FN Archimer Export Format
PT J
TI Learning latent dynamics for partially observed chaotic systems
BT 
AF Ouala, S.
   Nguyen, D.
   Drumetz, Lucas
   Chapron, Bertrand
   Pascual, A.
   Collard, Fabrice
   Gaultier, Lucile
   Fablet, Ronan
AS 1:1;2:1;3:1;4:2;5:3;6:4;7:4;8:1;
FF 1:;2:;3:;4:PDG-ODE-LOPS-SIAM;5:;6:;7:;8:;
C1 IMT Atlantique, UMR CNRS Lab-STICC, 29280 Plouzané, France
   Ifremer, LOPS, 29280 Plouzané, France
   IMEDEA, UIB-CSIC, 07190 Esporles, Spain
   OceanDataLab, 29280 Locmaria-Plouzané, France
C2 IMT ATLANTIQUE, FRANCE
   IFREMER, FRANCE
   IMEDEA, SPAIN
   OCEANDATALAB, FRANCE
SI BREST
SE PDG-ODE-LOPS-SIAM
UM LOPS
IN WOS Ifremer UMR
   copubli-france
   copubli-europe
IF 3.642
TC 18
UR https://archimer.ifremer.fr/doc/00657/76945/78151.pdf
LA English
DT Article
AB This paper addresses the data-driven identification of latent representations of partially observed dynamical systems, i.e., dynamical systems for which some components are never observed, with an emphasis on forecasting applications and long-term asymptotic patterns. Whereas state-of-the-art data-driven approaches rely in general on delay embeddings and linear decompositions of the underlying operators, we introduce a framework based on the data-driven identification of an augmented state-space model using a neural-network-based representation. For a given training dataset, it amounts to jointly reconstructing the latent states and learning an ordinary differential equation representation in this space. Through numerical experiments, we demonstrate the relevance of the proposed framework with respect to state-of-the-art approaches in terms of short-term forecasting errors and long-term behavior. We further discuss how the proposed framework relates to the Koopman operator theory and Takens’ embedding theorem. Delay embedding coordinates provide a simple tool for reconstructing a system limit cycle given partial observations of the dynamics. However, finding a parametric approximation of the dynamics based on the delay-embedded states is far from being straightforward since we do not have any relationships between the spanned limit cycle and a particular form of parametric models. In this work, we propose an alternative based on neural networks and automatic differentiation. We learn both the dynamics and the latent states jointly as a solution of an optimization problem 
PY 2020
PD OCT
SO Chaos
SN 1054-1500
PU AIP Publishing
VL 30
IS 10
UT 000585761000002
DI 10.1063/5.0019309
ID 76945
ER

EF