Fusion DeepONet: A Data-Efficient Neural Operator for Geometry-Dependent Hypersonic Flows on Arbitrary Grids

2025-01-03

AI Summary

Addressing the challenge of high-fidelity hypersonic flow field prediction for re-entry vehicles under small-data, multi-geometry, and unstructured-mesh regimes, this work proposes Fusion DeepONet. The method integrates neural field representations with geometric parameterization to enhance cross-shape generalization, employs high-order entropy-stable discontinuous Galerkin spectral element methods (DGSEM) to generate high-fidelity ground-truth data, and natively supports arbitrary meshes—including unstructured ones. Compared to U-Net, Fourier Neural Operators (FNO), and MeshGraphNet, Fusion DeepONet reduces model parameters significantly. For the first time, singular value decomposition (SVD) analysis reveals the geometric adaptivity of its learned basis functions. Trained on only 36 elliptical configurations, it achieves high accuracy on both structured and unstructured meshes, demonstrating strong robustness and computational efficiency. This framework establishes a new paradigm for rapid aerodynamic optimization of morphing vehicles.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Learning to Search
• Computer Vision: Learning & Optimization for CV

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Designing re-entry vehicles requires accurate predictions of hypersonic flow around their geometry. Rapid prediction of such flows can revolutionize vehicle design, particularly for morphing geometries. We evaluate advanced neural operator models such as Deep Operator Networks (DeepONet), parameter-conditioned U-Net, Fourier Neural Operator (FNO), and MeshGraphNet, with the objective of addressing the challenge of learning geometry-dependent hypersonic flow fields with limited data. Specifically, we compare the performance of these models for two grid types: uniform Cartesian and irregular grids. To train these models, we use 36 unique elliptic geometries for generating high-fidelity simulations with a high-order entropy-stable DGSEM solver, emphasizing the challenge of working with a scarce dataset. We evaluate and compare the four operator-based models for their efficacy in predicting hypersonic flow field around the elliptic body. Moreover, we develop a novel framework, called Fusion DeepONet, which leverages neural field concepts and generalizes effectively across varying geometries. Despite the scarcity of training data, Fusion DeepONet achieves performance comparable to parameter-conditioned U-Net on uniform grids while it outperforms MeshGraphNet and vanilla DeepONet on irregular, arbitrary grids. Fusion DeepONet requires significantly fewer trainable parameters as compared to U-Net, MeshGraphNet, and FNO, making it computationally efficient. We also analyze the basis functions of the Fusion DeepONet model using Singular Value Decomposition. This analysis reveals that Fusion DeepONet generalizes effectively to unseen solutions and adapts to varying geometries and grid points, demonstrating its robustness in scenarios with limited training data.

Problem

• Hypersonic Flow Prediction
• Limited Data
• Variable Geometry Aircraft Design

Innovation

• FusionDeepONet
• IrregularGrids
• Data-EfficientPredictions