This study proposes a new physics-constrained data-driven approach for sensitivity analysis and uncertainty quantification of large-scale chaotic Partial Differential Equations (PDEs). Unlike conventional sensitivity analysis, the proposed approach can manipulate the unsteady sensitivity function (i.e., tangent) for PDE-constrained optimizations. In this new approach, high-dimensional governing equations from physical space are transformed into an unphysical space (i.e., Hilbert space) to develop a closure model in the form of a Reduced-Order Model (ROM). This closure model is derived explicitly from the governing equations to set strong constraints on manifolds in Hilbert space. Afterward, a new data sampling method is proposed to build a data-driven approach for this framework. A series of least squares minimizations are set in the form of a novel auto-encoder system to solve this closure model. To compute sensitivities, least-squares shadowing minimization is applied to the ROM. It is shown that the proposed approach can capture sensitivities for large-scale chaotic dynamical systems, where finite difference approximations fail.
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Research Article| January 03 2022
Sensitivity analysis of chaotic dynamical systems using a physics-constrained data-driven approach
Hamid R. Karbasian ;
Hamid R. Karbasian, Brian C. Vermeire; Sensitivity analysis of chaotic dynamical systems using a physics-constrained data-driven approach. Physics of Fluids 1 January 2022; 34 (1): 014101. https://doi.org/10.1063/5.0076074
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