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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 (2022) Ensemble Kalman inversion for sparse learning of dynamical systems from time-averaged data. Journal of Computational Physics, 470 . Art. No. 111559. ISSN 0021-9991. doi:10.1016/

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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 timeseries 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.

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URLURL TypeDescription ItemDiscussion paper
Schneider, Tapio0000-0001-5687-2287
Stuart, Andrew M.0000-0001-9091-7266
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. This work was supported by the generosity of Eric and Wendy Schmidt by recommendation of the Schmidt Futures program, and the National Science Foundation (NSF, award AGS1835860). AMS is also supported by NSF (award DMS-1818977) and by the Office of Naval Research (award N00014-17-1-2079).
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Schmidt Futures ProgramUNSPECIFIED
Office of Naval Research (ONR)N00014-17-1-2079
Record Number:CaltechAUTHORS:20221013-45138000.1
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ID Code:117393
Deposited By: Research Services Depository
Deposited On:14 Oct 2022 19:56
Last Modified:14 Oct 2022 19:56

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