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Journal Article

Machine discovery of partial differential equations from spatiotemporal data: A sparse Bayesian learning framework

Authors

Yuan,  Ye
External Organizations;

Li,  Xiuting
External Organizations;

Li,  Liang
External Organizations;

Liang,  Frank
External Organizations;

Tang,  Xiuchuan
External Organizations;

Zhang,  Fumin
External Organizations;

Goncalves,  Jorge
External Organizations;

Voss,  Henning
External Organizations;

Ding,  Han
External Organizations;

/persons/resource/Juergen.Kurths

Kurths,  Jürgen
Potsdam Institute for Climate Impact Research;

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Citation

Yuan, Y., Li, X., Li, L., Liang, F., Tang, X., Zhang, F., Goncalves, J., Voss, H., Ding, H., Kurths, J. (2023): Machine discovery of partial differential equations from spatiotemporal data: A sparse Bayesian learning framework. - Chaos, 33, 11, 113122.
https://doi.org/10.1063/5.0160900


Cite as: https://publications.pik-potsdam.de/pubman/item/item_29325
Abstract
This study presents a general framework, namely, Sparse Spatiotemporal System Discovery (S3d⁠), for discovering dynamical models given by Partial Differential Equations (PDEs) from spatiotemporal data. S3d is built on the recent development of sparse Bayesian learning, which enforces sparsity in the estimated PDEs. This approach enables a balance between model complexity and fitting error with theoretical guarantees. The proposed framework integrates Bayesian inference and a sparse priori distribution with the sparse regression method. It also introduces a principled iterative re-weighted algorithm to select dominant features in PDEs and solve for the sparse coefficients. We have demonstrated the discovery of the complex Ginzburg–Landau equation from a traveling-wave convection experiment, as well as several other PDEs, including the important cases of Navier–Stokes and sine-Gordon equations, from simulated data.