Shivam Barwey

Shivam Barwey, Varun Shankar, Venkatasubramanian Viswanathan et al.

The goal of this work is to address two limitations in autoencoder-based models: latent space interpretability and compatibility with unstructured meshes. This is accomplished here with the development of a novel graph neural network (GNN) autoencoding architecture with demonstrations on complex fluid flow applications. To address the first goal of interpretability, the GNN autoencoder achieves reduction in the number nodes in the encoding stage through an adaptive graph reduction procedure. This reduction procedure essentially amounts to flowfield-conditioned node sampling and sensor identification, and produces interpretable latent graph representations tailored to the flowfield reconstruction task in the form of so-called masked fields. These masked fields allow the user to (a) visualize where in physical space a given latent graph is active, and (b) interpret the time-evolution of the latent graph connectivity in accordance with the time-evolution of unsteady flow features (e.g. recirculation zones, shear layers) in the domain. To address the goal of unstructured mesh compatibility, the autoencoding architecture utilizes a series of multi-scale message passing (MMP) layers, each of which models information exchange among node neighborhoods at various lengthscales. The MMP layer, which augments standard single-scale message passing with learnable coarsening operations, allows the decoder to more efficiently reconstruct the flowfield from the identified regions in the masked fields. Analysis of latent graphs produced by the autoencoder for various model settings are conducted using using unstructured snapshot data sourced from large-eddy simulations in a backward-facing step (BFS) flow configuration with an OpenFOAM-based flow solver at high Reynolds numbers.

Shivam Barwey, Pinaki Pal, Saumil Patel et al.

A graph neural network (GNN) approach is introduced in this work which enables mesh-based three-dimensional super-resolution of fluid flows. In this framework, the GNN is designed to operate not on the full mesh-based field at once, but on localized meshes of elements (or cells) directly. To facilitate mesh-based GNN representations in a manner similar to spectral (or finite) element discretizations, a baseline GNN layer (termed a message passing layer, which updates local node properties) is modified to account for synchronization of coincident graph nodes, rendering compatibility with commonly used element-based mesh connectivities. The architecture is multiscale in nature, and is comprised of a combination of coarse-scale and fine-scale message passing layer sequences (termed processors) separated by a graph unpooling layer. The coarse-scale processor embeds a query element (alongside a set number of neighboring coarse elements) into a single latent graph representation using coarse-scale synchronized message passing over the element neighborhood, and the fine-scale processor leverages additional message passing operations on this latent graph to correct for interpolation errors. Demonstration studies are performed using hexahedral mesh-based data from Taylor-Green Vortex and backward-facing step flow simulations at Reynolds numbers of 1600 and 3200. Through analysis of both global and local errors, the results ultimately show how the GNN is able to produce accurate super-resolved fields compared to targets in both coarse-scale and multiscale model configurations. Reconstruction errors for fixed architectures were found to increase in proportion to the Reynolds number. Geometry extrapolation studies on a separate cavity flow configuration show promising cross-mesh capabilities of the super-resolution strategy.

Shivam Barwey, Hojin Kim, Romit Maulik

Data-driven 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 interpretability enhancement procedure for GNNs, with application to unstructured mesh-based fluid dynamics modeling. Given a black-box baseline GNN model, the end result is an interpretable GNN model that isolates regions in physical space, corresponding to sub-graphs, that are intrinsically linked to the forecasting task while retaining the predictive capability of the baseline. These structures identified by the interpretable GNNs are adaptively produced in the forward pass and serve as explainable links between the baseline model architecture, the optimization goal, and known problem-specific physics. Additionally, through a regularization procedure, the interpretable 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 field data sourced from flow over a backward-facing step at high Reynolds numbers, with geometry extrapolations demonstrated for ramp and wall-mounted cube configurations.

Kiran Yalamanchi, Shivam Barwey, Ibrahim Jarrah et al.

Computational fluid dynamics (CFD) simulations of complex fluid flows in energy systems are prohibitively expensive due to strong nonlinearities and multiscale-multiphysics interactions. In this work, we present a transformer-based modeling framework for prediction of fluid flows, and demonstrate it for high-pressure gas injection phenomena relevant to reciprocating engines. The approach employs a hierarchical Vision Transformer (SwinV2-UNet) architecture that processes multimodal flow datasets from multi-fidelity simulations. The model architecture is conditioned on auxiliary tokens explicitly encoding the data modality and time increment. Model performance is assessed on two different tasks: (1) spatiotemporal rollouts, where the model autoregressively predicts the flow state at future times; and (2) feature transformation, where the model infers unobserved fields/views from observed fields/views. We train separate models on multimodal datasets generated from in-house CFD simulations of argon jet injection into a nitrogen environment, encompassing multiple grid resolutions, turbulence models, and equations of state. The resulting data-driven models learn to generalize across resolutions and modalities, accurately forecasting the flow evolution and reconstructing missing flow-field information from limited views. This work demonstrates how large vision transformer-based models can be adapted to advance predictive modeling of complex fluid flow systems.

Shivam Barwey, Pinaki Pal

Super-resolution flow reconstruction using state-of-the-art data-driven techniques is valuable for a variety of applications, such as subgrid/subfilter closure modeling, accelerating spatiotemporal forecasting, data compression, and serving as an upscaling tool for sparse experimental measurements. In the present work, a first-of-its-kind multiscale graph transformer approach is developed for mesh-based super-resolution (SR-GT) of reacting flows. The novel data-driven modeling paradigm leverages a graph-based flow-field representation compatible with complex geometries and non-uniform/unstructured grids. Further, the transformer backbone captures long-range dependencies between different parts of the low-resolution flow-field, identifies important features, and then generates the super-resolved flow-field that preserves those features at a higher resolution. The performance of SR-GT is demonstrated in the context of spectral-element-discretized meshes for a challenging test problem of 2D detonation propagation within a premixed hydrogen-air mixture exhibiting highly complex multiscale reacting flow behavior. The SR-GT framework utilizes a unique element-local (+ neighborhood) graph representation for the coarse input, which is then tokenized before being processed by the transformer component to produce the fine output. It is demonstrated that SR-GT provides high super-resolution accuracy for reacting flow-field features and superior performance compared to traditional interpolation-based SR schemes.

Riddhiman Raut, Romit Maulik, Shivam Barwey

This work presents a novel graph neural network (GNN) architecture, the Feature-specific Interpretable Graph Neural Network (FIGNN), designed to enhance the interpretability of deep learning surrogate models defined on unstructured grids in scientific applications. Traditional GNNs often obscure the distinct spatial influences of different features in multivariate prediction tasks. FIGNN addresses this limitation by introducing a feature-specific pooling strategy, which enables independent attribution of spatial importance for each predicted variable. Additionally, a mask-based regularization term is incorporated into the training objective to explicitly encourage alignment between interpretability and predictive error, promoting localized attribution of model performance. The method is evaluated for surrogate modeling of two physically distinct systems: the SPEEDY atmospheric circulation model and the backward-facing step (BFS) fluid dynamics benchmark. Results demonstrate that FIGNN achieves competitive predictive performance while revealing physically meaningful spatial patterns unique to each feature. Analysis of rollout stability, feature-wise error budgets, and spatial mask overlays confirm the utility of FIGNN as a general-purpose framework for interpretable surrogate modeling in complex physical domains.

Varun Shankar, Shivam Barwey, Zico Kolter et al.

Graph neural networks (GNNs) have shown promise in learning unstructured mesh-based simulations of physical systems, including fluid dynamics. In tandem, geometric deep learning principles have informed the development of equivariant architectures respecting underlying physical symmetries. However, the effect of rotational equivariance in modeling fluids remains unclear. We build a multi-scale equivariant GNN to forecast fluid flow and study the effect of modeling invariant and non-invariant representations of the flow state. We evaluate the model performance of several equivariant and non-equivariant architectures on predicting the evolution of two fluid flows, flow around a cylinder and buoyancy-driven shear flow, to understand the effect of equivariance and invariance on data-driven modeling approaches. Our results show that modeling invariant quantities produces more accurate long-term predictions and that these invariant quantities may be learned from the velocity field using a data-driven encoder.

Shivam Barwey, Venkat Raman

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.

Shivam Barwey, Malik Hassanaly, Venkat Raman et al.

This work utilizes data-driven methods to morph a series of time-resolved experimental OH-PLIF images into corresponding three-component planar PIV fields in the closed domain of a premixed swirl combustor. The task is carried out with a fully convolutional network, which is a type of convolutional neural network (CNN) used in many applications in machine learning, alongside an existing experimental dataset which consists of simultaneous OH-PLIF and PIV measurements in both attached and detached flame regimes. Two types of models are compared: 1) a global CNN which is trained using images from the entire domain, and 2) a set of local CNNs, which are trained only on individual sections of the domain. The locally trained models show improvement in creating mappings in the detached regime over the global models. A comparison between model performance in attached and detached regimes shows that the CNNs are much more accurate across the board in creating velocity fields for attached flames. Inclusion of time history in the PLIF input resulted in small noticeable improvement on average, which could imply a greater physical role of instantaneous spatial correlations in the decoding process over temporal dependencies from the perspective of the CNN. Additionally, the performance of local models trained to produce mappings in one section of the domain is tested on other, unexplored sections of the domain. Interestingly, local CNN performance on unseen domain regions revealed the models' ability to utilize symmetry and antisymmetry in the velocity field. Ultimately, this work shows the powerful ability of the CNN to decode the three-dimensional PIV fields from input OH-PLIF images, providing a potential groundwork for a very useful tool for experimental configurations in which accessibility of forms of simultaneous measurements are limited.