Bulletin of the American Physical Society
75th Annual Meeting of the Division of Fluid Dynamics
Volume 67, Number 19
Sunday–Tuesday, November 20–22, 2022; Indiana Convention Center, Indianapolis, Indiana.
Session A28: CFD: Uncertainty Quantification and Machine Learning 
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Chair: Zhao Pan, University of Waterloo Room: 237 
Sunday, November 20, 2022 8:00AM  8:13AM 
A28.00001: Data assimilation using particle filters in reducedorder model subspaces Aishah Albarakati, Marko Budisic, Colin Roberts, Erik S Van Vleck Particle filters are a class of data assimilation techniques that can estimate the state and uncertainty of dynamical models by combining nonlinear evolution models with nongaussian uncertainty distributions. However, estimating high dimensional states, such as those associated with spatiallydiscretized models, requires an exponentiallylarge size of estimation ensemble to avoid the socalled filter collapse, which dramatically decreases efficiency of the estimation. By combining particle filters with projectionbased datadriven model reduction techniques, such as Proper Orthogonal Decomposition and Dynamic Mode Decomposition, we demonstrate that it is possible to reduce the effective dimension of the models and staveoff the filter collapse for a class of dynamical models relevant to forecasting of geophysical fluid flows. This technique can be adapted to account for models with transient change in parameters, by windowed building of the projection matrices. We demonstrate several variants of the technique on Lorenz’96type models and on a simulation of shallowwater equations. 
Sunday, November 20, 2022 8:13AM  8:26AM 
A28.00002: Dataassisted uncertainty quantification and extreme event prediction in climate models using physicallyconsistent neural networks. AlexisTzianni Charalampopoulos, Shixuan Zhang, Ruby Leung, Themistoklis Sapsis We present a novel approach for improving the predictions of statistical quantities for turbulent systems, with focus on climate models. The method utilizes neural networks to learn a mapping between highfidelity reference data and nudged coarsescale simulations. Then, during testing, freerunning coarse scale data are used as input for the model, with the corrected timeseries having statistics that approximate that of the reference data. The ability to transfer the mapping the model has learned during training with nudged input data to freerunning data during testing is achieved by (a) a novel appropriate spectral nudging method and (b) incorporation of physical constraints during training. These constraints are vital for capturing the correct statistics of climate models, while the proposed nudging allows for a scheme that generalizes well when used on outofsample data. The method is first validated on a 2layer quasigeostrophic model, a prototypical system mimicking baroclinic instability in midlatitude and highlatitude atmospheric flows. After that, the model is tested on realistic freerunning, coarsescale climate simulations of Earth's atmosphere. Predictions of extreme events like tropical cyclones, extratropical cyclones and atmospheric rivers are presented. The model agrees well with reference data, outperforming standard climate closure schemes computationally. 
Sunday, November 20, 2022 8:26AM  8:39AM 
A28.00003: Extracting NavierStokes solutions from noisy data with physicsconstrained convolutional neural networks Daniel Kelshaw, Luca Magri Experimental fluid measurements, such as those from PIV and immersed probes, may be corrupted with noise. In this work, we propose a method to extract the solution to the NavierStokes equations from noisy and biased data. We introduce the physicsinformed convolutional neural network, capable of embedding prior knowledge of the physics in the form of governing equations. This enables us to produce a mapping from the corruptedobservations to the solution of NavierStokes equations. Ultimately, this provides the tools required to extract underlying truesolutions to partial differential equations in general. 
Sunday, November 20, 2022 8:39AM  8:52AM 
A28.00004: Hierarchical Bayesian multifidelity modelling applied to turbulent flows Philipp Schlatter, Saleh Rezaeiravesh, Timofey Mukha Conducting highfidelity studies in fluid mechanics can be prohibitively expensive, particularly at high Reynolds numbers. Thus, it is necessary to develop accurate yet costeffective models for outerloop problems involving turbulent flows. One way is multifidelity models (MFMs) which aim at accurately predicting quantities of interest (QoIs) and their stochastic moments by combining the data obtained from different fidelities. 
Sunday, November 20, 2022 8:52AM  9:05AM Not Participating 
A28.00005: Probabilistic surrogate modeling of unsteady fluid dynamics using deep graph normalizing flows Luning Sun, JianXun Wang Surrogate modeling of spatiotemporal physics based on graph neural networks (GNN) has recently attracted increasing attention in the scientific machine learning community due to the flexibility of graphs in dealing with unstructured data. However, the model prediction often contains considerable uncertainty originated from data sparsity, noise, and model forms, which are critical in realworld applications but have yet been considered in existing works. In this work, we propose a novel probabilistic surrogate model, graph normalizing flows (GNFFluids), to accurately predict fluid dynamics with quantified uncertainties. Specifically, a novel message passing scheme is proposed to efficiently compute the Jacobian matrix in normalizing flows. A spatial encoderdecoder structure is constructed to compactly represent the flow fields in the meshreduced space. Moreover, an attentionbased model is used for capturing longterm temporal structures. The proposed model is demonstrated on several complex flows, and the performance is compared with existing competitive stateoftheart baseline models in terms of predictive accuracy and uncertainty quantification capability. 
Sunday, November 20, 2022 9:05AM  9:18AM 
A28.00006: Neural networks for multifidelity ensemble largeeddy simulations Mark Benjamin, Stefan P Domino, Gianluca Iaccarino The computing expense of uncertainty quantification or optimization in computational fluid dynamics can be reduced by using two levels of solution fidelity: one that is high  such as a highresolution largeeddy simulation (LES)  and one that is low  such as a coarse resolution LES. In this work, we explore a method that uses information from the higher fidelity level to inform the lower fidelity simulations using neural networks. This learned function is a source term in the momentum equations of the low fidelity simulations, and is trained to account for the discretization and filtering errors incurred. We explore different choices of features and training methodology, and evaluate the performance of the method in wallbounded turbulence. 
Sunday, November 20, 2022 9:18AM  9:31AM 
A28.00007: Quantifying uncertainty in largeeddy simulation results of a natural river flow Kevin Flora, Ali Khosronejad Highfidelity numerical modeling of rivers requires many assumptions related to implementing the environmental heterogeneity of the channel boundaries and flow dynamics which introduce uncertainty into the model results. Specifically, uncertainty in the stream discharge, channel roughness and inclusion of, vegetation can influence the distribution of flow in a river. To address the effect of trees on the flow field, we have employed a vegetation model to remove momentum from the flow using a depth dependent drag coefficient which is also a source of uncertainty. For determining the combined uncertainty of the results, we use repeated largescale eddy simulations over a range of discharges, roughness and vegetation parameters on a reach of the American River, California. Using the polynomial chaos expansion and Monte Carlo sampling techniques, we express the uncertainty as confidence intervals in the spanwise flow velocities, velocity profiles and bed shear stresses in the river. Sobol indices have been determined to provide an estimate of the relative influence of each unknown input parameter. 
Sunday, November 20, 2022 9:31AM  9:44AM 
A28.00008: Uncertainty Propagation in CFD Simulations using NonIntrusive Polynomial Chaos Expansion and Reduced Order Modeling Nikhil Iyengar, Dimitri Mavris, Dushhyanth Rajaram Uncertainty propagation in expensive simulations, such as computational fluid dynamics, with highdimensional outputs is challenging due to limited training data and prohibitive computational evaluation costs. Proper Orthogonal Decomposition (POD) is a popular linear dimension reduction method used in reduced order modeling (ROM) to enable the rapid prediction of uncertain outputs. However, achieving parametric robustness is particularly challenging in problems that exhibit strong nonlinearities, discontinuities, and gradients. This study presents a nonintrusive, nonlinear ROM which combines manifold learning with sparse polynomial chaos expansions to enable uncertainty propagation in highdimensional fields with nonlinear features. The study evaluates the performance of both global and local manifold learning methods, such as Isometric Mapping and Locally Linear Embedding, against the POD on two numerical examples, including twodimensional supersonic flow around the RAE2822 airfoil with uncertainties in geometry and flow conditions. These methods are benchmarked against Monte Carlo simulations to quantify the impact of polynomial order and sample count on the predicted mean, standard deviation, and uncertainty distributions for both linear and nonlinear ROMs. 
Sunday, November 20, 2022 9:44AM  9:57AM 
A28.00009: RoseNNa: A performant library for portable neural network inference with application to CFD Ajay Bati, Spencer H Bryngelson

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