Emulator embedded neural networks, which are a type of physics informed neural network, leverage multi-fidelity data sources for efficient design exploration of aerospace engineering systems. Multiple realizations of the neural network models are trained with different random initializations. The ensemble of model realizations is used to assess epistemic modeling uncertainty caused due to 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.

翻译：嵌入仿真器的神经网络作为物理信息神经网络的一种，利用多保真度数据源进行航空航天工程系统的高效设计探索。通过不同随机初始化训练多个神经网络模型实例，这些模型实例的集成用于评估因训练样本不足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目标导向自适应学习至关重要。然而，集成模型的训练成本往往过高，在自适应学习过程中若模型无法并行训练时，将带来计算挑战。本研究提出一种基于快速神经网络范式的新型嵌入仿真器神经网络。与通过梯度反向传播优化所有网络层权重与偏置的传统神经网络训练不同，快速神经网络训练仅通过线性回归技术调整最后一层连接权重。结果表明，所提出的嵌入仿真器神经网络可实现近乎瞬时的训练，且通常不损失预测精度。通过多个解析算例及通用高超声速飞行器的航空航天飞行参数研究验证了所提方法的有效性。