Forward sensitivity analysis and mode dependent control for closure modeling of Galerkin systems. (English) Zbl 1538.65334
Summary: Model reduction by projection-based approaches is often associated with losing some of the important features that contribute towards the dynamics of the retained scales. As a result, a mismatch occurs between the predicted trajectories of the original system and the truncated one. We put forth a framework to apply a continuous time control signal in the latent space of the reduced order model (ROM) to account for the effect of truncation. We set the control input using parameterized models by following energy transfer principles. Our methodology relies on observing the system behavior in the physical space and using the projection operator to restrict the feedback signal into the latent space. Then, we leverage the forward sensitivity method (FSM) to derive relationships between the feedback and the desired mode-dependent control. We test the performance of the proposed approach using two test cases, corresponding to viscous Burgers and vortex merger problems at high Reynolds number. Results show that the ROM trajectory with the applied FSM control closely matches its target values in both the data-dense and data-sparse regimes.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 76F65 | Direct numerical and large eddy simulation of turbulence |
| 76F20 | Dynamical systems approach to turbulence |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 65M99 | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 93B30 | System identification |
Keywords:
reduced order models; forward sensitivity; inverse problem; latent control; outer-loop applications; sparse sensorsReferences:
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