Session T29: CFD: Data-Driven and Machine Learning

Machine learning framework to predict flows over arbitrarily arranged solid arrays

Flow past an array of solid obstacles have been studied in a wide range of fluid engineering applications, such as heat exchanger, particulate filter, and fuel cells. Existing studies have focused on flows over homogeneous arrangements with different geometrical setups and attained the explicit correlation between the inlet and outlet. However, it is impractical to obtain the explicit correlation in flows over heterogeneous arrangements due to the case-specific nature for countless geometries. In the present study, we devised a machine learning framework to tackle the case-specific nature in flows over arbitrarily arranged solid arrays, including heterogeneous arrangements. The training datasets can be generated systematically and automatically with recursively performed CFD simulations, without the need to set up all possible geometric configurations of a solid array. The prediction performance with high robustness was verified by comparison of the predicted results to the target data retrieved from the numerical simulations in various geometries and flow regimes. Furthermore, we also showed that the proposed model can cover untrained flow regimes.   

A Neural Differentiable Solver for Efficient Simulation of Fluid-Structure Interaction

Solving complex fluid-solid interactions (FSI) phenomena is crucial in many science and engineering applications. Classical CFD-based solvers are too expensive to tackle the large-scale simulation demands. The ever-increasing data availability and rapid developments in deep learning (DL) have opened new avenues to tackle the challenges by integrating deep neural networks (DNN) into traditional numerical solvers, enabling effective data-driven modeling. In this regard, we established a fully differentiable programming framework for simulating FSI problems based on JAX. The fluid is solved by direct numerical simulation (DNS), and the solid is immersed in the fluid field through the direct forcing method. Specifically, the velocity inside an immersed solid is interpolated by a sinusoidal function. As the framework is entirely built in JAX with auto-differentiation (AD) capability, different DNN models can be easily integrated and optimized within the numerical solver as a whole in an end-to-end manner. Several benchmark cases are studied to demonstrate the merit and potential of the proposed method for efficient FSI modeling.   

Competitive physics-informed networks for high-accuracy solutions to Navier-Stokes problems

Physics Informed Neural Networks (PINNs) represent partial differential equations (PDEs) as neural networks, solving these PDEs to an accuracy of around 10^-3 L₂ relative error via Adam-based optimizers. Competitive Physics Informed Neural Networks (CPINNs) were recently introduced by the authors to enable training to at least single-precision accuracy (10^-7). They are based on an adversarial approach to training, which amounts to a minimax optimization problem, that relaxes the poor conditioning of the differential operators that comprise the PDE. Here, we apply the CPINN strategy to solve canonical Navier-Stokes problems with high accuracy.   

β-Variational autoencoders for nonlinear and ortogonal reduced-order models in turbulence

In this work we propose a deep-learning framework for learning a minimal and near-orthogonal set of non-linear modes in the context of turbulent flows. In particular, we focus on a high-fidelity numerical database of a simplified urban environment (Lazpita et al., Phys. Fluids 34, 051702, 2022). The proposed technique relies on β-variational autoencoders (β-VAEs) and convolutional neural networks (CNNs), which enable extracting non-linear modes while encouraging the learning of statistically-independent latent variables and penalizing the size of the latent vector. Moreover, we introduce an algorithm for ordering the resulting modes with respect to their contribution to the reconstruction. We demonstrate that by constraining the shape of the latent space, it is possible to motivate orthogonality and extract a set of parsimonious modes which enable high-quality reconstruction. Our results show the excellent performance of the method in the reconstruction against linear-theory-based decompositions, where the energy percentage captured by the proposed method from five modes is equal to 87.36% against 32.41% from POD. Furthermore, we show the ability of our approach to extract near-orthogonal modes with the determinant of the correlation matrix, which is equal to 0.99, thus enhancing the interpretability of the obtained reduced-order models (ROMs).

    

Accelerating Poisson equation solvers with physics informed neural networks

Poisson equations are a class of partial differential equations (PDEs) encountered in several areas of physics, from fluid mechanics to electrostatics. Iterative solvers, such as multigrid and conjugate gradient algorithms, are commonly employed to solve Poisson equations but become computationally expensive and require an increasing number of iterations for large problems. In this work, we focus on the pressure equation encountered within the pressure-velocity coupling for incompressible flows, which ensures a divergence-free velocity field. We train physics-informed neural networks (PINNs) to solve the pressure equation, taking spatial coordinates and source terms as model inputs. Our model is easily parallelised and agnostic to mesh resolution, allowing us to train on data from coarse grids and predict on resolved cases in parallel. We deploy the trained Tensorflow model within the pimpleFoam solver in OpenFOAM and observe a reduction in pressure solver iterations when using the neural network predictions as an initial guess for the linear solver compared to using the previous pressure field. We then study the performance impact of using PINNs as a first guess and investigate optimal conditions for their use with linear solvers.   

Efficient high-dimensional variational data assimilation with machine-learned reduced-order models

Data assimilation (DA) in geophysical sciences remains the cornerstone of robust forecasts from numerical models. Indeed, DA plays a crucial role in the quality of numerical weather prediction and is a crucial building block that has allowed dramatic improvements in weather forecasting over the past few decades. DA is commonly framed in a variational setting, where one solves an optimization problem within a Bayesian formulation using raw model forecasts as a prior and observations as likelihood. This leads to a DA objective function that needs to be minimized, where the decision variables are the initial conditions specified to the model. In traditional DA, the forward model is numerically and computationally expensive. Here we replace the forward model with a low-dimensional, data-driven, and differentiable emulator. Consequently, gradients of our DA objective function with respect to the decision variables are obtained rapidly via automatic differentiation. We demonstrate our approach by performing an emulator-assisted DA forecast of geopotential height. Our results indicate that emulator-assisted DA is faster than traditional equation-based DA forecasts by 4 orders of magnitude, allowing computations to be performed on a workstation rather than a dedicated high-performance computer. In addition, we describe accuracy benefits of emulator-assisted DA when compared to simply using the emulator for forecasting (i.e., without DA).   

Hydrokinetic turbine wake flow reconstruction in large-scale waterways using physics-informed convolutional neural networks

We developed a physics-informed autoencoder convolutional neural network (CNN) to reconstruct the 3D time-averaged velocity field and turbulence kinetic energy of the wake flow of hydrokinetic turbines using the instantaneous high-fidelity simulation data. To ensure the prediction results follow the physics laws, mass and momentum conservation equations are embedded into the loss function of the CNN model. The CNN is trained using the large eddy simulation (LES) result of the wake flow of a single row of turbines. Then the validation is conducted using the LES results of overlapping and staggered cases of two rows of turbines. The results show good agreement between the LES and CNN algorithms while the CNN requires only a small fraction of the computational costs of the LES.   

On the application of data-driven modeling within the rotorcraft design space

For highly iterative rotorcraft-based design tasks, such as design optimization or trajectory prediction, it is essential that there exists an aerodynamic model capable of providing an accurate representation of turbulent flow fields at a minimal computational expense. While high-fidelity computational fluid dynamics (CFD) has been proven capable of providing accurate aerodynamic predictions, for rotorcraft-based applications CFD's large computational expense has greatly limited its integration into highly iterative design tasks.This study will investigate the feasibility of leveraging proper orthogonal decomposition (POD) and convolutional neural networks (CNNs) for surrogate modeling within the rotorcraft design space. Surrogate modeling techniques are applied to both surface flow and rotorcraft wake modeling. For surface flow modeling, rotorcraft-based store separation is simulated using CFD from which both POD and CNN based surrogate models are generated for surface pressure and shear stress load distributions. Surrogate model predictions are coupled with the equations of motion to provide store trajectory replications. For rotor wake modeling, an isolated rotor is simulated in hover. Surrogate models are derived using both POD and CNN from which flow field reconstructions and predictions are generated.   

Efficient and Robust Training Strategies for Physics and Equality Constrained Artificial Neural Networks

Deep neural networks trained on governing physical laws have shown significant promise in solving forward and inverse problems. However, several issues remain challenging for developing models that are trustworthy and produce physically feasible predictions. A common approach in formulating a physics-informed objective function is to aggregate a weighted sum of the residual form of a governing partial differential equation (PDE) and its boundary conditions. The weights that balance the interplay between each objective term are problem specific and not known a-priori. In previous work, we have demonstrated that the formulation of the objective function as a constrained optimization problem is critically significant and proposed physics and equality constrained artificial neural networks (PECANNs) to successfully learn the solution of PDEs for a variety of problems. In PECANNs, we employ the Augmented Lagrangian method (ALM) to enforce equality constraints on the PDE loss. Previously, we gradually updated the penalty parameter until a maximum safeguarding value was reached for all constraints. However, finding an optimal strategy to update the penalty parameter as well as setting a proper safeguarding penalty parameter remained a challenge. In this work, we propose a novel strategy to adaptively learn a penalty parameter for every constraint without setting a safeguarding penalty parameter. Additionally, we refine the formulation of the constrained optimization problem to enable mini-batch training and reduce its computer memory footprint for large-scale PDE problems. We apply our method to several challenging benchmark problems and demonstrate marked improvement over existing methods.   

Prediction and Control of 2D Decaying Turbulence using Generative Adversarial Networks

In the current study, dynamics prediction of freely decaying 2D turbulence has been performed based on generative adversarial networks (GANs). Our prediction model, PredictionNet, showed high accuracy up to one integral time scale where the autocorrelation drops to around 0.25 with a correlation coefficient of 0.855. It also showed much higher accuracy on the enstrophy spectrum than the baseline convolutional neural network (CNN) model. By checking small-scale statistics and performing scale decomposition to investigate and quantify such differences in the predictive accuracy, we found that the GAN model can reflect the statistical properties and small-scale features of turbulence very well. In addition, as an example of applications, we used our PredictionNet as a surrogate model for the task of flow control. The control model, ControlNet, was capable of finding optimum disturbances that change the time-evolution of the flow field to a direction that fits an objective function, such as maximizing the propagation of the control effect. Although it is the prediction and control of relatively simple 2D turbulence, the current study results provide a new approach to the dynamics prediction and flow control that can be applied to more complex turbulence.   

A heterogeneous computing approach to coupled simulation and machine-learning deployment for high-speed flows

This work studies real-time integration of computational fluid dynamics (CFD) simulations and machine learning (ML) tasks, and its application to parameter estimation of high-speed multi-component flows in chemical propulsion systems. Our approach leverages implicit task-based parallelism through the Legion runtime ecosystem to efficiently execute expensive PDE solvers on GPUs and ML tasks on CPUs, on heterogeneous supercomputers. To achieve parallel performance without cumbersome implementation, we combine an in-house compressible flow solver written in Regent, a Legion-API endowed with a CUDA code generator, and Python-based ML algorithms in Pygion, a Legion-API retaining the flexibility of Python while permitting the use of its immense ML ecosystem. In the application, the solver generates an ensemble of transient, high-speed, turbulent jets of multi-component mixtures. The ML tasks simultaneously extract subsets of the data and feed them to an ensemble of deep-neural networks for on-line training and for the Bayesian estimation of flow parameters. The influences of both the ensemble data size and the ensemble model size on the accuracy of estimation are discussed.   

Machine Learning Flux-Limiters for Compressible Flow Simulations

The Euler equations governing inviscid compressible flow have a rich history of research devoted to solving them numerically. The main difficulty lays in the potential for singularities caused by shocks forming within the flow field, which necessitate the use of low-order numerical schemes to avoid introducing large, erroneous oscillations into the solution.  A popular approach for circumventing this oscillation problem is the use of flux-limiters, which aim to mix low-order and high-order flux representations such that no oscillations are generated near shocks, while high-order accuracy is maintained in smooth regions of the flow. Over the last several decades, numerous flux-limiter schemes have been proposed, largely by varying the mixing function that changes with the local solution smoothness. Here, we propose using a machine-learned flux-limiter to blend low-order and high-order fluxes. The resulting flux-limiter is then applied across multiple coarse-graining levels derived from higher-resolution solution data. Its effectiveness is assessed across a suite of common one-dimensional test cases and compared against popular flux-limiters, such as min-mod, van Leer, and superbee.

This abstract is approved for release under LA-UR-22-27187.