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Ensemble Kalman Inversion for Sparse Learning of Dynamical Systems from Time-Averaged Data

Schneider, Tapio and Stuart, Andrew M. and Wu, Jin-Long (2020) Ensemble Kalman Inversion for Sparse Learning of Dynamical Systems from Time-Averaged Data. . (Unpublished)

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Enforcing sparse structure within learning has led to significant advances in the field of data-driven discovery of dynamical systems. However, such methods require access not only to time-series of the state of the dynamical system, but also to the time derivative. In many applications, the data are available only in the form of time-averages such as moments and autocorrelation functions. We propose a sparse learning methodology to discover the vector fields defining a (possibly stochastic or partial) differential equation, using only time-averaged statistics. Such a formulation of sparse learning naturally leads to a nonlinear inverse problem to which we apply the methodology of ensemble Kalman inversion (EKI). EKI is chosen because it may be formulated in terms of the iterative solution of quadratic optimization problems; sparsity is then easily imposed. We then apply the EKI-based sparse learning methodology to various examples governed by stochastic differential equations (a noisy Lorenz 63 system), ordinary differential equations (Lorenz 96 system and coalescence equations), and a partial differential equation (the Kuramoto-Sivashinsky equation). The results demonstrate that time-averaged statistics can be used for data-driven discovery of differential equations using sparse EKI. The proposed sparse learning methodology extends the scope of data-driven discovery of differential equations to previously challenging applications and data-acquisition scenarios.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper ItemJournal Article
Schneider, Tapio0000-0001-5687-2287
Alternate Title:Imposing Sparsity Within Ensemble Kalman Inversion
Additional Information:We thank Melanie Bieli, Tobias Bischoff and Anna Jaruga for sharing their formulation of the moment-based coalescence equation, and for discussions about it. All authors are supported by the generosity of Eric and Wendy Schmidt by recommendation of the Schmidt Futures program, by Earthrise Alliance, Mountain Philanthropies, the Paul G. Allen Family Foundation, and the National Science Foundation (NSF, award AGS1835860). A.M.S. is also supported by NSF (award DMS-1818977) and by the Office of Naval Research (award N00014-17-1-2079).
Funding AgencyGrant Number
Schmidt Futures ProgramUNSPECIFIED
Earthrise AllianceUNSPECIFIED
Mountain PhilanthropiesUNSPECIFIED
Paul G. Allen Family FoundationUNSPECIFIED
Office of Naval Research (ONR)N00014-17-1-2079
Subject Keywords:Ensemble Kalman inversion, sparse learning, dynamical systems, time-averaged data
Record Number:CaltechAUTHORS:20201109-141011032
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106562
Deposited By: George Porter
Deposited On:09 Nov 2020 22:38
Last Modified:14 Oct 2022 19:27

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