Session A28: CFD: Uncertainty Quantification and Machine Learning

Data assimilation using particle filters in reduced-order model subspaces

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 non-gaussian uncertainty distributions. However, estimating high dimensional states, such as those associated with spatially-discretized models, requires an exponentially-large size of estimation ensemble to avoid the so-called filter collapse, which dramatically decreases efficiency of the estimation. By combining particle filters with projection-based data-driven 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 stave-off 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’96-type models and on a simulation of shallow-water equations.

    

Data-assisted uncertainty quantification and extreme event prediction in climate models using physically-consistent neural networks.

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 high-fidelity reference data and nudged coarse-scale simulations. Then, during testing, free-running coarse- scale data are used as input for the model, with the corrected time-series 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 free-running 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 out-of-sample data. The method is first validated on a 2-layer quasigeostrophic model, a prototypical system mimicking baroclinic instability in mid-latitude and high-latitude atmospheric flows. After that, the model is tested on realistic free-running, coarse-scale 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.   

Extracting Navier-Stokes solutions from noisy data with physics-constrained convolutional neural networks

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 Navier-Stokes equations from noisy and biased data. We introduce the physics-informed 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 corrupted-observations to the solution of Navier-Stokes equations. Ultimately, this provides the tools required to extract underlying true-solutions to partial differential equations in general.

We showcase this methodology on three physical systems: linear convection-diffusion, non-linear convection-diffusion, and the 2D turbulent Kolmogorov flow. We find that the proposed methodology is capable of removing arbitrary spatially-varying bias, beyond simple stochastic variations in the data, for each system studied. Beyond this, we investigate the robustness of the methodology to multi-modality, magnitude, and form of the corruption - results being agnostic in each case.

This work opens opportunities for the extraction of Navier-Stokes solutions from PIV data and the detection of faulty sensors that introduce biases.   

Hierarchical Bayesian multifidelity modelling applied to turbulent flows

Conducting high-fidelity studies in fluid mechanics can be prohibitively expensive, particularly at high Reynolds numbers. Thus, it is necessary to develop accurate yet cost-effective models for outer-loop 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. 

When constructing MFMs, a balance is sought between a few expensive (but accurate) simulations and many more inexpensive (but potentially less accurate) simulations. Two main characteristics have to be considered. 1) there is a distinguishable hierarchy in the fidelity of approaches such as Reynolds-averaged Navier-Stokes simulation (RANS), hybrid RANS-LES, wall-modeled and wall-resolved LES, and DNS. 2) the outcome of any of these approaches can be potentially uncertain due to various inherent uncertainties.

In our multifidelity modeling approach, the calibration parameters as well as the hyperparameters appearing in the Gaussian processes are simultaneously estimated within a Bayesian framework. GP provides a natural way for incorporating observational uncertainty in the data. The Bayesian inference is done using a Markov Chain Monte Carlo (MCMC) approach.

The efficiency of the HC-MFM is evaluated for various problems involving turbulent flows. We first predict the lift coefficient of a wing at Reynolds number 1.6M. The flow angle of attack (AoA) is the design parameter and the data fed into the MFM comprises of: wind-tunnel experiments, detached-eddy simulations (DES) and 2D RANS. Turbulence intensity and the stall AoA is considered as a calibration parameter. We will also study the periodic hill case to assess the effect of geometry, and provide comparison to more classical co-Krigin approaches.

    

Not Participating

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 real-world applications but have yet been considered in existing works. In this work, we propose a novel probabilistic surrogate model, graph normalizing flows (GNF-Fluids), 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 encoder-decoder structure is constructed to compactly represent the flow fields in the mesh-reduced space. Moreover, an attention-based model is used for capturing long-term temporal structures. The proposed model is demonstrated on several complex flows, and the performance is compared with existing competitive state-of-the-art baseline models in terms of predictive accuracy and uncertainty quantification capability.   

Neural networks for multi-fidelity ensemble large-eddy simulations

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 high-resolution large-eddy 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 wall-bounded turbulence.   

Quantifying uncertainty in large-eddy simulation results of a natural river flow

High-fidelity 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 large-scale 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.

    

Uncertainty Propagation in CFD Simulations using Non-Intrusive Polynomial Chaos Expansion and Reduced Order Modeling

Uncertainty propagation in expensive simulations, such as computational fluid dynamics, with high-dimensional 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 non-linearities, discontinuities, and gradients. This study presents a non-intrusive, nonlinear ROM which combines manifold learning with sparse polynomial chaos expansions to enable uncertainty propagation in high-dimensional 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 two-dimensional 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.   

RoseNNa: A performant library for portable neural network inference with application to CFD

Computational fluid dynamics practitioners have witnessed a dramatic growth in neural-network-based models for traditional closures and numerical methods. The networks are usually trained and tested in high-level languages like Python via PyTorch, TensorFlow, or other  packages. Unfortunately, it is challenging to efficiently evaluate such opaque models in current large-scale CFD solvers, which are typically written in derivatives of C or Fortran. As a result, few studies of large machine-learning-assisted fluid dynamics solvers exist. We introduce a Fortran-based library called RoseNNa as a step towards solving this problem. It implements the functionality of the most common neural network architectures used or proposed for CFD. RoseNNa interprets ONNX representations of neural network models, which can be exported from most machine learning libraries and thus promotes usability. RoseNNa is linked to the user’s codebase at compile-time via usual means. The API exposes the neural network inputs and outputs to the user to be minimally invasive to existing code.