用于空气动力学预测的先进深度学习架构评估
Evaluation of State-of-the-Art Deep Learning Architectures for Aerodynamical Predictions
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中文总结 AI 辅助
本文对四种先进算子学习模型在航空航天工程应用能力进行基准测试，通过两个实验评估其预测二维翼型和三维飞机构型表面压力分布的能力，分析各模型优缺点，推动基于人工智能的代理建模领域发展，突出Bi-Stride多尺度图神经网络和Transolver(++)的前景。
中文摘要 AI 辅助
代理模型用于在经典数值求解器计算成本过高的工程应用中替代它们。例如在空气动力学中，此类模型在形状优化和载荷分析等问题上为计算流体动力学提供了经济高效的替代方案。一种基于深度学习的代理模型——算子学习模型，直接逼近物理现象背后偏微分方程的解算子。本文通过对四种先进的算子学习模型在航空航天工程应用能力方面进行全面基准测试，推进了基于人工智能的代理方法研究。在两个实验中，评估了模型预测不同复杂程度二维翼型表面压力分布以及工业规模三维飞机构型表面压力分布的能力，包括捕捉解中的不连续性（激波）、对大量网格点的可扩展性以及处理数据稀缺性的能力。通过仔细分析，研究结果为基于人工智能的代理建模领域提供了各架构优缺点的详细见解，推动了该领域发展，尤其强调了Bi-Stride多尺度图神经网络和Transolver(++)是有前景的空气动力学应用代理模型。
英文摘要
Surrogate models are used to substitute classical numerical solvers in engineering applications where the computational cost of the latter becomes infeasible. For instance, in aerodynamics such models offer cost-effective alternatives to computational fluid dynamics in problems such as shape optimization and load analysis, which oftentimes require high-fidelity simulations for a multitude of different parameter combinations. A specific class of deep learning-based surrogate models termed operator learning models directly approximates the solution operators to the partial differential equations underlying the physical phenomenon, thereby learning to replicate solutions to entire families of problems. However, while nowadays numerous architectures of this type get published, corresponding benchmark studies remain scarce. In this article, we advance the study of AI-based surrogate methods by thoroughly benchmarking four state-of-the-art operator learning models on their aptitude for applications in aerospace engineering. In two experiments, we assess the models' capabilities of predicting the surface pressure distribution on two-dimensional airfoil shapes of varying complexity and on an industrial-scale three-dimensional aircraft configuration. Thereby, we evaluate the models' abilities to fulfill frequent requirements in aerodynamics such as capturing discontinuities (shocks) in the solutions, scalability towards excessive amounts of mesh points and handling of data scarcity. Accompanied by a careful analysis, our findings drive forward the field of AI-based surrogate modeling by providing detailed insights into the strengths and weaknesses of the individual architectures, thus allowing to identify priorities for future developments. In particular the Bi-Stride Multi-Scale Graph Neural Network and Transolver(++) are highlighted as promising surrogate models for aerodynamical applications.
