skip to main content

This content will become publicly available on July 1, 2023

Title: Physics-Based Regression vs. CFD for Hagen-Poiseuille and Womersley Flows and Uncertainty Quantification
Computational fluid dynamics (CFD) and its uncertainty quantification are computationally expensive. We use Gaussian Process (GP) methods to demonstrate that machine learning can build efficient and accurate surrogate models to replace CFD simulations with significantly reduced computational cost without compromising the physical accuracy. We also demonstrate that both epistemic uncertainty (machine learning model uncertainty) and aleatory uncertainty (randomness in the inputs of CFD) can be accommodated when the machine learning model is used to reveal fluid dynamics. The demonstration is performed by applying simulation of Hagen-Poiseuille and Womersley flows that involve spatial and spatial-tempo responses, respectively. Training points are generated by using the analytical solutions with evenly discretized spatial or spatial-temporal variables. Then GP surrogate models are built using supervised machine learning regression. The error of the GP model is quantified by the estimated epistemic uncertainty. The results are compared with those from GPU-accelerated volumetric lattice Boltzmann simulations. The results indicate that surrogate models can produce accurate fluid dynamics (without CFD simulations) with quantified uncertainty when both epistemic and aleatory uncertainties exist.
; ; ;
Brehm, Christoph; Pandya, Shishir
Award ID(s):
Publication Date:
Journal Name:
Eleventh International Conference on Computational Fluid Dynamics (ICCFD11)
Page Range or eLocation-ID:
1 - 11
Sponsoring Org:
National Science Foundation
More Like this
  1. Gaussian process (GP) emulator has been used as a surrogate model for predicting force field and molecular potential, to overcome the computational bottleneck of ab initio molecular dynamics simulation. Integrating both atomic force and energy in predictions was found to be more accurate than using energy alone, yet it requires O(( NM) 3 ) computational operations for computing the likelihood function and making predictions, where N is the number of atoms and M is the number of simulated configurations in the training sample due to the inversion of a large covariance matrix. The high computational cost limits its applications to the simulation of small molecules. The computational challenge of using both gradient information and function values in GPs was recently noticed in machine learning communities, whereas conventional approximation methods may not work well. Here, we introduce a new approach, the atomized force field model, that integrates both force and energy in the emulator with many fewer computational operations. The drastic reduction in computation is achieved by utilizing the naturally sparse covariance structure that satisfies the constraints of the energy conservation and permutation symmetry of atoms. The efficient machine learning algorithm extends the limits of its applications on larger molecules undermore »the same computational budget, with nearly no loss of predictive accuracy. Furthermore, our approach contains an uncertainty assessment of predictions of atomic forces and energies, useful for developing a sequential design over the chemical input space.« less
  2. Learning reservoir flow dynamics is of primary importance in creating robust predictive models for reservoir management including hydraulic fracturing processes. Physics-based models are to a certain extent exact, but they entail heavy computational infrastructure for simulating a wide variety of parameters and production scenarios. Reduced-order models offer computational advantages without compromising solution accuracy, especially if they can assimilate large volumes of production data without having to reconstruct the original model (data-driven models). Dynamic mode decomposition (DMD) entails the extraction of relevant spatial structure (modes) based on data (snapshots) that can be used to predict the behavior of reservoir fluid flow in porous media. In this paper, we will further enhance the application of the DMD, by introducing sparse DMD and local DMD. The former is particularly useful when there is a limited number of sparse measurements as in the case of reservoir simulation, and the latter can improve the accuracy of developed DMD models when the process dynamics show a moving boundary behavior like hydraulic fracturing. For demonstration purposes, we first show the methodology applied to (flow only) single- and two-phase reservoir models using the SPE10 benchmark. Both online and offline processes will be used for evaluation. We observe thatmore »we only require a few DMD modes, which are determined by the sparse DMD structure, to capture the behavior of the reservoir models. Then, we applied the local DMDc for creating a proxy for application in a hydraulic fracturing process. We also assessed the trade-offs between problem size and computational time for each reservoir model. The novelty of our method is the application of sparse DMD and local DMDc, which is a data-driven technique for fast and accurate simulations.« less
  3. Modern digital manufacturing processes, such as additive manufacturing, are cyber-physical in nature and utilize complex, process-specific simulations for both design and manufacturing. Although computational simulations can be used to optimize these complex processes, they can take hours or days--an unreasonable cost for engineering teams leveraging iterative design processes. Hence, more rapid computational methods are necessary in areas where computation time presents a limiting factor. When existing data from historical examples is plentiful and reliable, supervised machine learning can be used to create surrogate models that can be evaluated orders of magnitude more rapidly than comparable finite element approaches. However, for applications that necessitate computationally- intensive simulations, even generating the training data necessary to train a supervised machine learning model can pose a significant barrier. Unsupervised methods, such as physics- informed neural networks, offer a shortcut in cases where training data is scarce or prohibitive. These novel neural networks are trained without the use of potentially expensive labels. Instead, physical principles are encoded directly into the loss function. This method substantially reduces the time required to develop a training dataset, while still achieving the evaluation speed that is typical of supervised machine learning surrogate models. We propose a new method formore »stochastically training and testing a convolutional physics-informed neural network using the transient 3D heat equation- to model temperature throughout a solid object over time. We demonstrate this approach by applying it to a transient thermal analysis model of the powder bed fusion manufacturing process.« less
  4. Abstract Computational fluid dynamics (CFD) modeling of left ventricle (LV) flow combined with patient medical imaging data has shown great potential in obtaining patient-specific hemodynamics information for functional assessment of the heart. A typical model construction pipeline usually starts with segmentation of the LV by manual delineation followed by mesh generation and registration techniques using separate software tools. However, such approaches usually require significant time and human efforts in the model generation process, limiting large-scale analysis. In this study, we propose an approach toward fully automating the model generation process for CFD simulation of LV flow to significantly reduce LV CFD model generation time. Our modeling framework leverages a novel combination of techniques including deep-learning based segmentation, geometry processing, and image registration to reliably reconstruct CFD-suitable LV models with little-to-no user intervention.1 We utilized an ensemble of two-dimensional (2D) convolutional neural networks (CNNs) for automatic segmentation of cardiac structures from three-dimensional (3D) patient images and our segmentation approach outperformed recent state-of-the-art segmentation techniques when evaluated on benchmark data containing both magnetic resonance (MR) and computed tomography(CT) cardiac scans. We demonstrate that through a combination of segmentation and geometry processing, we were able to robustly create CFD-suitable LV meshes from segmentationsmore »for 78 out of 80 test cases. Although the focus on this study is on image-to-mesh generation, we demonstrate the feasibility of this framework in supporting LV hemodynamics modeling by performing CFD simulations from two representative time-resolved patient-specific image datasets.« less
  5. Purpose The purpose of this work is to investigate the similarity requirements for the application of multifidelity modeling (MFM) for the prediction of airfoil dynamic stall using computational fluid dynamics (CFD) simulations. Design/methodology/approach Dynamic stall is modeled using the unsteady Reynolds-averaged Navier–Stokes equations and Menter's shear stress transport turbulence model. Multifidelity models are created by varying the spatial and temporal discretizations. The effectiveness of the MFM method depends on the similarity between the high- (HF) and low-fidelity (LF) models. Their similarity is tested by computing the prediction error with respect to the HF model evaluations. The proposed approach is demonstrated on three airfoil shapes under deep dynamic stall at a Mach number 0.1 and Reynolds number 135,000. Findings The results show that varying the trust-region (TR) radius (λ) significantly affects the prediction accuracy of the MFM. The HF and LF simulation models hold similarity within small (λ ≤ 0.12) to medium (0.12 ≤ λ ≤ 0.23) TR radii producing a prediction error less than 5%, whereas for large TR radii (0.23 ≤ λ ≤ 0.41), the similarity is strongly affected by the time discretization and minimally by the spatial discretization. Originality/value The findings of this work present new knowledge for the construction of accurate MFMs for dynamic stall performance predictionmore »using LF model spatial- and temporal discretization setup and the TR radius size. The approach used in this work is general and can be used for other unsteady applications involving CFD-based MFM and optimization.« less