Jacobian-Scaled K-means Clustering for Physics-Informed Segmentation of Reacting Flows

This work introduces Jacobian-scaled K-means (JSK-means) clustering, which is a physics-informed clustering strategy centered on the K-means framework. The method allows for the injection of underlying physical knowledge into the clustering procedure through a distance function modification: instead of leveraging conventional Euclidean distance vectors, the JSK-means procedure operates on distance vectors scaled by matrices obtained from dynamical system Jacobians evaluated at the cluster centroids. The goal of this work is to show how the JSK-means algorithm -- without modifying the input dataset -- produces clusters that capture regions of dynamical similarity, in that the clusters are redistributed towards high-sensitivity regions in phase space and are described by similarity in the source terms of samples instead of the samples themselves. The algorithm is demonstrated on a complex reacting flow simulation dataset (a channel detonation configuration), where the dynamics in the thermochemical composition space are known through the highly nonlinear and stiff Arrhenius-based chemical source terms. Interpretations of cluster partitions in both physical space and composition space reveal how JSK-means shifts clusters produced by standard K-means towards regions of high chemical sensitivity (e.g., towards regions of peak heat release rate near the detonation reaction zone). The findings presented here illustrate the benefits of utilizing Jacobian-scaled distances in clustering techniques, and the JSK-means method in particular displays promising potential for improving former partition-based modeling strategies in reacting flow (and other multi-physics) applications

Interpretable Fine-Tuning for Graph Neural Network Surrogate Models

Data-based surrogate modeling has surged in capability in recent years with the emergence of graph neural networks (GNNs), which can operate directly on mesh-based representations of data. The goal of this work is to introduce an interpretable fine-tuning strategy for GNNs, with application to unstructured mesh-based fluid dynamics modeling. The end result is a fine-tuned GNN that adds interpretability to a pre-trained baseline GNN through an adaptive sub-graph sampling strategy that isolates regions in physical space intrinsically linked to the forecasting task, while retaining the predictive capability of the baseline. The structures identified by the fine-tuned GNNs, which are adaptively produced in the forward pass as explicit functions of the input, serve as an accessible link between the baseline model architecture, the optimization goal, and known problem-specific physics. Additionally, through a regularization procedure, the fine-tuned GNNs can also be used to identify, during inference, graph nodes that correspond to a majority of the anticipated forecasting error, adding a novel interpretable error-tagging capability to baseline models. Demonstrations are performed using unstructured flow data sourced from flow over a backward-facing step at high Reynolds numbers

Data-Driven Modeling of Compressible Reacting Flow Using Hardware-Oriented Algorithms

High-fidelity numerical simulations of combustion processes in next-generation hypersonic propulsion devices (including, but not limited to, rotating detonation engines and scramjets) play a crucial role in enabling robust design strategies for their real-world deployment. These simulations, however, require full-geometry numerical solutions of the compressible reacting Navier-Stokes equations. Spatiotemporal resolution requirements stemming from multi-scale interactions between turbulence, shockwaves, and chemical reactions contained in these governing equations induce computationally prohibitive bottlenecks that render the required long-time resolved simulations of these propulsion devices infeasible. A particularly elusive bottleneck comes from the treatment of detailed chemical kinetics required to accurately describe the time evolution of species concentrations and flow-chemistry interactions within the combustors. The computational hurdles emerge here from the arithmetic intensity of chemical source term evaluations and immense disparities in chemical timescales for practical fuels. The goal of this work is to provide a physics-guided data-driven modeling strategy for accelerating high-fidelity compressible reacting flow solvers via elimination of the chemistry bottleneck. Since unsteady features of interest in compressible reacting flow (e.g. detonations) are sustained by chemical reactions, the principle assumption is that local regions in the thermochemical state space can be used to classify spatially coherent regions of dynamical similarity within the reacting flowfield in physical space. Based on this assumption, the modeling approach finds these local regions using an unsupervised clustering algorithm and deploys targeted models for accelerated chemical source term evaluation within each region. The novelty comes from (a) ensuring that flowfield classifications enabled by the clustering procedure are consistent with physical expectations in complex compressible reacting flow (e.g. the clusters identify meaningful regions within detonation wave structure in rotating detonation engines), and (b) embedding physical knowledge directly into the clustering objective function. Emphasis is placed on ensuring the modeling framework can be extended to in-situ (or online) integration with flow solvers, such that the method is not tied down to single geometric configurations. Additional steps are taken to ensure that the algorithms used in the modeling approach are compatible with modern high-performance computing trends dominated by GPU-centric node architectures.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/174384/1/sbarwey_1.pd

A Neural Network-Inspired Matrix Formulation of Chemical Kinetics for Acceleration on GPUs

High-fidelity simulations of turbulent flames are computationally expensive when using detailed chemical kinetics. For practical fuels and flow configurations, chemical kinetics can account for the vast majority of the computational time due to the highly non-linear nature of multi-step chemistry mechanisms and the inherent stiffness of combustion chemistry. While reducing this cost has been a key focus area in combustion modeling, the recent growth in graphics processing units (GPUs) that offer very fast arithmetic processing, combined with the development of highly optimized libraries for artificial neural networks used in machine learning, provides a unique pathway for acceleration. The goal of this paper is to recast Arrhenius kinetics as a neural network using matrix-based formulations. Unlike ANNs that rely on data, this formulation does not require training and exactly represents the chemistry mechanism. More specifically, connections between the exact matrix equations for kinetics and traditional artificial neural network layers are used to enable the usage of GPU-optimized linear algebra libraries without the need for modeling. Regarding GPU performance, speedup and saturation behaviors are assessed for several chemical mechanisms of varying complexity. The performance analysis is based on trends for absolute compute times and throughput for the various arithmetic operations encountered during the source term computation. The goals are ultimately to provide insights into how the source term calculations scale with the reaction mechanism complexity, which types of reactions benefit the GPU formulations most, and how to exploit the matrix-based formulations to provide optimal speedup for large mechanisms by using sparsity properties. Overall, the GPU performance for the species source term evaluations reveals many informative trends with regards to the effect of cell number on device saturation and speedup. Most importantly, it is shown that the matrix-based method enables highly efficient GPU performance across the board, achieving near-peak performance in saturated regimes

A generative adversarial network (GAN) approach to creating synthetic flame images from experimental data

Modern diagnostic tools in turbulent combustion allow for highly-resolved measurements of reacting flows; however, they tend to generate massive data-sets, rendering conventional analysis intractable and inefficient. To alleviate this problem, machine learning tools may be used to, for example, discover features from the data for downstream modeling and prediction tasks. To this end, this work applies generative adversarial networks (GANs) to generate realistic flame images based on a time-resolved data set of hydroxide concentration snapshots obtained from planar laser induced fluorescence measurements of a model combustor. The generative model is able to generate flames in attached, lifted, and intermediate configurations dictated by the user. Using k-means clustering and proper orthogonal decomposition, the synthetic image set produced by the GAN is shown to be visually similar to the real image set, with recirculation zones and burned/unburned regions clearly present, indicating good GAN performance in capturing the experimental data statistical structure. Combined with techniques for controlling the configuration of generated flames, this work opens new avenues towards tractable statistical analysis and modeling of flame behavior, as well as rapid and inexpensive flame data generation

Segmentation of high-speed flow fields using physics-informed clustering

The advent of data-based modeling has provided new methods and algorithms for analyzing the complex flow fields in high-speed combustion applications. These techniques can be used to study the fluid dynamics and reaction progress in different regions of the flow, which can provide insight into the underlying physics of the system while helping one identify avenues for the development and application of new models. The present work implements two such algorithms – the standard K-means clustering algorithm and a modified Jacobian-scaled K-means clustering algorithm – to analyze a high-speed reacting flow field. The results show that the Jacobian-scaled K-means algorithm allocates more clusters in the regions of the thermochemical state space where chemical source term is highest. In physical space, this concentrates the flow partitions in regions where heat release rate is higher and chemical timescales are lower. This is observed for different cluster numbers and data sets. When moving between data sets that occupy different portions of the state space, the cluster centroid locations are found to be less sensitive to the data set when the Jacobian-scaled K-means algorithm is used. Altogether, the modified K-means algorithm provides a new tool for identifying thermodynamic and thermochemical similarities in and across compressible reactive flow fields