Complex optimal design and control processes often require repeated evaluations of expensive objective functions and consist of large design spaces. Data-driven surrogates such as neural networks and Gaussian processes provide an attractive alternative to simulations and are utilized frequently to represent these objective functions in optimization. However, pure data-driven models, due to a lack of adherence to basic physics laws and constraints, are often poor at generalizing and extrapolating. This is particularly the case, when training occurs over sparse high-fidelity datasets. A class of Physics-infused machine learning (PIML) models integrate ML models with low-fidelity partial physics models to improve generalization performance while retaining computational efficiency. This paper presents two potential approaches for Physics infused modelling of aircraft aerodynamics which incorporate Artificial Neural Networks with a low-fidelity Vortex Lattice Method model with blown wing effects (BLOFI) to improve prediction performance while also keeping the computational cost tractable. This paper also develops an end-to-end auto differentiable open-source framework that enables efficient training of such hybrid models. These two PIML modelling approaches are then used to predict the aerodynamic coefficients of a 6 rotor eVTOL aircraft given its control parameters and flight conditions. The models are trained on a sparse high-fidelity dataset generated using a CHARM model. The trained models are then compared against the vanilla low-fidelity model and a standard pure data-driven ANN. Our results show that one of the proposed architectures outperforms all the other models at a nominal increase in run time. These results are promising and pave way for PIML frameworks which can generalize over different aircraft and configurations thereby significantly reducing costs of design and control.

翻译：复杂优化设计与控制过程通常需要反复评估高代价目标函数，且涉及大规模设计空间。尽管神经网络和高斯过程等数据驱动代理模型为模拟提供了极具吸引力的替代方案，并常被用于优化中表征这些目标函数，但纯数据驱动模型由于缺乏对基本物理定律与约束的遵循，在泛化与外推方面表现欠佳——尤其在基于稀疏高保真数据集进行训练时更为突出。物理知识融合机器学习（PIML）模型通过将机器学习模型与低保真度局部物理模型相结合，在保持计算效率的同时提升泛化性能。本文提出两种适用于飞行器气动特性的物理知识融合建模方法，该方法将人工神经网络与带吹翼效应的低保真度涡格法（BLOFI）模型相结合，在提升预测性能的同时保持计算成本可控。本文还构建了支持高效训练此类混合模型的端到端自动微分开源框架。随后采用这两种PIML建模方法，基于控制参数与飞行条件预测六旋翼电动垂直起降（eVTOL）飞行器的气动系数。模型使用CHARM模型生成的稀疏高保真数据集进行训练，并与原始低保真度模型及标准纯数据驱动人工神经网络进行对比。结果表明，其中一种架构在运行时间略有增加的情况下，综合性能优于所有其他模型。这些成果为构建可跨不同飞行器构型泛化的PIML框架奠定了基础，有望显著降低设计与控制成本。