Mini-Symposium 6

7th Annual Meeting of SIAM Central States Section

7th Annual Meeting of SIAM Central States Section

MS06: Data-driven fluid dynamics

Organizer:

Omer San, Oklahoma State University

Session A: Oct.2, 10:30am-11:50am, Classroom Building 106

MS06-A-1 10:30am-10:50am (Oct 2) CLB 106	Pedram Hashem Dabaghian, Oklahoma State University	Nonintrusive reduced order modeling of convective Boussinesq flows
	We formulate three nonintrusive methods and systematically explore their performance in terms of the ability to reconstruct the quantities of interest and their predictive capabilities. The methods include deterministic dynamic mode decomposition (DDMD), randomized dynamic mode decomposition (RDMD) and nonlinear proper orthogonal decomposition (NLPOD). The first two of which are based on the Koopman approximation theory while the third one is a coupled unsupervised and supervised machine learning approach. We apply these methods to a convection dominated fluid flow problem governed by the Boussinesq equations where a fluid with two different temperatures blend together in generating vast variety of vortex patterns evolving in time. We analyze the reconstruction results primarily at two different times. At the earlier time of the flow evolution where there is a relatively fewer fine scale vortical structures, our results indicate that both DMD approaches monotonically decrease errors as we increase the number of retained modes. At a later stage, however, DMD reconstruction error monotonically increases with increasing the number of modes. In contrast, we do not observe such monotonic behavior in the NLPOD approach. These observations can be related to the suboptimal selection of the relevant hyperparameters that intensify overfitting issues. Overall, our results indicate that, with a proper selection of number of retained modes and neural network architectures, all three approaches make predictions that are in a good agreement with the full order model solution.
MS06-A-2 10:50am-11:10am (Oct 2) CLB 106	Saeed Akbari, Oklahoma State University	Nonlinear proper orthogonal decomposition approach for modeling Rayleigh Bénard convection
	In recent years, many nonintrusive reduced order modeling (NIROM) approaches have been developed in computing science where machine learning algorithms are employed to build inexpensive but accurate surrogate models. In this regard, we present a nonlinear proper orthogonal decomposition (POD) framework, denoted as NLPOD, to build a NIROM for spatio-temporal dynamical systems. POD is a mature NIROM method that projects the high dimensional data into a low-rank but linear manifold, which produces a considerable projection error for highly nonlinear convection-dominated flows. In this study, we aim at using an autoencoder (AE) neural network to break nonlinear correlations and reduce the projection error. We first utilize the POD to forge a linear latent space for modeling Rayleigh Bénard convection, and then, employ the AE to further compress POD temporal coefficients through an unsupervised mapping. The long short-term memory technology is utilized to predict future states in the low-rank manifold.
MS06-A-3 11:10am-11:30am (Oct 2) CLB 106	Mehrdad Zomorodiyan, Oklahoma State University	Automatic Mixed-Precision (AMP) Computational Fluid Dynamics (CFD)
	Nvidia has developed half-precision (FP16) Tensor Cores that operate at 12 times the speed of their double-precision (FP64) cores. In popular deep-learning frameworks, you can already take advantage of Tensor Cores with AMP module and a few adjustments in your code to speed up the training process 2-6 times without losing accuracy for various models. In this work, I solve a simple CFD problem in two modes: single-precision (FP32) as our baseline and mixed-precision (FP16/FP32) as an attempt to leverage Tensor Cores for a faster run. The goal is to use FP16 for everything unless it affects the accuracy; Some operations/tensors must be FP32 as they hold too wide of a range of values to fit in FP16 without clipping. However, other variables can fit in FP16 with proper scaling. Like AMP, I would go over a range of values for a single scaler to fit an operation/tensor into FP16 range. If no such scaler is found that part should run on FP32.
MS06-A-4 11:30am-11:50am (Oct 2) CLB 106	Shafi Romeo, Oklahoma State University	Fluid flow modeling in elastic networking tubes
	In diagnosis of heart disease, such as atherosclerosis, arrhythmia or hyper-tension, blood flow rate and pressure are good indicators for the presence of blockage in the arteries. One-dimensional modelling of the human cardiovascular system based on the Pulsed Flow Equations (PFE) can be useful in predicting the dynamics of blood flow propagation through these arterial elastic tubes. Here, the consequent nonlinear coupled system of equations is solved by the finite-differences methods like Lax-Wendroff scheme and is then applied to an open 1D axisymmetric model arterial network of the human vascular system containing the largest 55 arteries. The critical effect of the nonlinear term in bifurcation points in the network have been solved with iterative schemes (e.g., Newton-Raphson method). Moreover, the various lumped parameter outflow boundary conditions for distal terminal points are also analyzed. The results indicate that the proposed numerical model can be used as an effective tool for investigating the dynamics of reduced-order models of flows in physiological systems and would be a good candidate for the macroscopic level of description of geometric multiscale of physiological systems.