Nonintrusive reduced order modeling framework for quasigeostrophic turbulence

Abstract

In this study, we present a non-intrusive reduced order modeling (ROM) framework for largescale quasi-stationary systems. The framework proposed herein exploits the time series prediction capability of long short-term memory (LSTM) recurrent neural network architecture such that: (i) in the training phase, the LSTM model is trained on the modal coefficients extracted from the highresolution data snapshots using proper orthogonal decomposition (POD) transform, and (ii) in the testing phase, the trained model predicts the modal coefficients for the total time recursively based on the initial time history. Hence, no prior information about the underlying governing equations is required to generate the ROM. To illustrate the predictive performance of the proposed framework, the mean flow fields and time series response of the field values are reconstructed from the predicted modal coefficients by using an inverse POD transform. As a representative benchmark test case, we consider a two-dimensional quasi-geostrophic (QG) ocean circulation model which, in general, displays an enormous range of fluctuating spatial and temporal scales. We first illustrate that the conventional Galerkin projection based reduced order modeling of such systems requires a high number of POD modes to obtain a stable flow physics. In addition, ROM-GP does not seem to capture the intermittent bursts appearing in the dynamics of the first few most energetic modes. However, the proposed non-intrusive ROM framework based on LSTM (ROM-LSTM) yields a stable solution even for a small number of POD modes. We also observe that the ROM-LSTM model is able to capture quasi-periodic intermittent bursts accurately, and yields a stable and accurate mean flow dynamics using the time history of a few previous time states, denoted as the lookback time-window in this paper. Throughout the paper, we demonstrate our findings in terms of time series evolution of the field values and mean flow patterns, which suggest that the proposed fully non-intrusive ROM framework is robust and capable of predicting noisy nonlinear fluid flows in an extremely efficient way compared to the conventional projection based ROM framework.

Digital Twin: Values, Challenges and Enablers From a Modeling Perspective

“…Alternatively, nonintrusive data-driven models (lying at the intersection of big data and data-driven models in Fig. 6) have emerged recently with the democratization of computational power, explosion of archival data, and advances in ML algorithms [284]- [294]. These approaches mostly involve matrix operations, which can be very efficiently parallelized on affordable GPU and TPU giving several orders of magnitude speedup as required in real-time applications.…”

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

“…where L, I and N are the linear, identity and nonlinear operators in (22), respectively. The above equation (27) can be written more explicitly…”

“…Now, given the desired state U , we use K-dimensional system of of nonlinear ordinary differential equations (24) to determine reduced-order solutions of the Navier-Stokes system. Approximations of solutions a (n) k of the system of ordinary differential equation (27) are determined using a fourth order Adams-Moulton method. To quantify the performance of different frameworks, we defined the root mean squared error (RMSE) between the FOM velocity field and the velocity field computed with different ROM frameworks.…”

“…8 shows a sketch of Long Short-Term Memory unit and an architecture of LSTM network training. For more details for LSTM architecture, one can refer to the articles [27] and references therein. Programs obtained from GitHub, namely ETC-ROM Master, Hybrid-Modeling Master, UROM Master and mnni-rom Master, are adopted, modified and used in the learning process.…”

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

“…where C is the correction given by Equation 8. We use three lookbacks to be consistent with AB3 scheme during training (please see the details in [45]). Since, GP modal coefficients are used as input features to the LSTM network, the parameter µ governing the system's behavior is taken implicitly into account.…”