Emulator embedded neural networks, which are closely related to physics informed neural networks, leverage multi-fidelity data sources for efficient design exploration of aerospace engineering systems. Multiple realizations of the neural network model are trained with different random initializations. The ensemble of model realizations is used to assess epistemic modeling uncertainty caused by a lack of training samples. This uncertainty estimation is crucial information for successful goal-oriented adaptive learning in an aerospace system design exploration. However, the costs of training the ensemble models often become prohibitive and pose a computational challenge, especially when the models are not trained in parallel during adaptive learning. In this work, a new type of emulator embedded neural network is presented using the rapid neural network paradigm. Unlike the conventional neural network training that optimizes the weights and biases of all the network layers by using gradient-based backpropagation, rapid neural network training adjusts only the last layer connection weights by applying a linear regression technique. It is found that the proposed emulator embedded neural network trains near-instantaneously, typically without loss of prediction accuracy. The proposed method is demonstrated on multiple analytical examples, as well as an aerospace flight parameter study of a generic hypersonic vehicle.

仿真器嵌入式神经网络与物理通知神经网络密切相关，利用多保真数据源进行航空航天工程系统的高效设计探索。使用不同的随机初始化来训练神经网络模型的多种实现。模型实现的集合用于评估由于缺乏训练样本而导致的认知建模不确定性。这种不确定性估计对于航空航天系统设计探索中成功的面向目标的自适应学习至关重要。然而，训练集成模型的成本往往变得过高，并带来计算挑战，特别是当模型在自适应学习期间没有并行训练时。在这项工作中，使用快速神经网络范例提出了一种新型的模拟器嵌入式神经网络。与使用基于梯度的反向传播来优化所有网络层的权重和偏差的传统神经网络训练不同，快速神经网络训练通过应用线性回归技术仅调整最后一层连接权重。研究发现，所提出的模拟器嵌入式神经网络训练几乎是瞬时的，通常不会损失预测精度。所提出的方法在多个分析示例以及通用高超音速飞行器的航空航天飞行参数研究中进行了演示。