Concurrent multi-parameter learning demonstrated on the Kuramoto-Sivashinsky equation

Abstract

We develop an algorithm based on the nudging data assimilation scheme for the concurrent (on-the-fly) estimation of scalar parameters for a system of evolutionary dissipative partial differential equations in which the state is partially observed. The algorithm takes advantage of the error that results from nudging a system with incorrect parameters with data from the true system. The intuitive nature of the algorithm makes its extension to several different systems immediate, and it allows for recovery of multiple parameters simultaneously. We test the method on the Kuramoto-Sivashinsky equation in one dimension and demonstrate its efficacy in this context.

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• The Bleeps, the Sweeps, and the Creeps: Convergence Rates for Dynamic Observer Patterns via Data Assimilation for the 2D Navier-Stokes Equations
• Interpretable structural model error discovery from sparse assimilation increments using spectral bias-reduced neural networks: A quasi-geostrophic turbulence test case
• Remarks on the stabilization of large-scale growth in the 2D Kuramoto-Sivashinsky equation
• Continuous data assimilation for hydrodynamics: consistent discretization and application to moment recovery