An Evolve-Then-Correct Reduced Order Model for Hidden Fluid Dynamics

Abstract

In this paper, we put forth an evolve-then-correct reduced order modeling approach that combines intrusive and nonintrusive models to take hidden physical processes into account. Specifically, we split the underlying dynamics into known and unknown components. In the known part, we first utilize an intrusive Galerkin method projected on a set of basis functions obtained by proper orthogonal decomposition. We then formulate a recurrent neural network emulator based on the assumption that observed data is a manifestation of all relevant processes. We further enhance our approach by using an orthonormality conforming basis interpolation approach on a Grassmannian manifold to address off-design conditions. The proposed framework is illustrated here with the application of two-dimensional co-rotating vortex simulations under modeling uncertainty. The results demonstrate highly accurate predictions underlining the effectiveness of the evolve-thencorrect approach toward realtime simulations, where the full process model is not known a priori.

Efficient computations for linear feedback control problems for target velocity matching of Navier-Stokes flows via POD and LSTM-ROM

“…which are used in [25] and [26], respectively. In theory, they are different but we can not find the differences in computational performance.…”

“…11). In step 5, interpolation techniques such as Grassman manifold interpolation [3,4,25], or the discrete empirical interpolation method, (DEIM) are typically applied to postprocess the results. For this work, however, such interpolations were not applied, so as to focus on the effects obtained from the Deep Learning technique.…”

“…Machine learning (ML) tools have had considerable success in the fluid mechanics community, identifying basic structures and mimicking dynamics [3,7,25,26]. However, modeling with ML, especially deep learning, has faced strict opposition from both academia and industry alike because it can produce non-physical results due to its black box nature and its lack of interpretability and generalization [10,23].…”

Forward sensitivity approach for estimating eddy viscosity closures in nonlinear model reduction

“…I, closure approaches based on physical significance have been usually relied on the analogy between LES and ROMs, e.g., the addition of an artificial viscosity term [81]. Recently, data-driven closure methods have been also pursued, e.g., using variational multiscale techniques [89,106,107], machine learning algorithms [108][109][110][111], and polynomial approximations [112,113].…”

A nudged hybrid analysis and modeling approach for realtime wake-vortex transport and decay prediction

“…To alleviate the problems associated with the existing WV models, data-driven machine learning methods might appear attractive at a first glance, but their limited interpretability owing to their black-box nature make them a misfit for the kind of safety-critical application under consideration. To this end, building upon our recent works on the hybrid analysis and modeling (HAM) framework [9][10][11], we present a data assimilation-empowered approach to utilize a machine learning methodology to fuse computationally-light physics-based models with the available real-time measurement data to provide more accurate and reliable predictions of wake-vortex transport and decay. In particular, we build a surrogate reduced order model (ROM), by combining proper orthogonal decomposition (POD) for basis construction [12][13][14][15][16][17] and Galerkin projection to model the dynamical evolution on the corresponding low-order subspace [18][19][20][21][22][23][24][25][26].…”