In high-speed flow past a normal shock, the fluid temperature rises rapidly triggering downstream chemical dissociation reactions. The chemical changes lead to appreciable changes in fluid properties, and these coupled multiphysics and the resulting multiscale dynamics are challenging to resolve numerically. Using conventional computational fluid dynamics (CFD) requires excessive computing cost. Here, we propose a totally new efficient approach, assuming that some sparse measurements of the state variables are available that can be seamlessly integrated in the simulation algorithm. We employ a special neural network for approximating nonlinear operators, the DeepONet [23], which is used to predict separately each individual field, given inputs from the rest of the fields of the coupled multiphysics system. We demonstrate the effectiveness of DeepONet for a benchmark hypersonic flow involving seven field variables. Specifically we predict five species in the non-equilibrium chemistry downstream of a normal shock at high Mach numbers as well as the velocity and temperature fields. We show that upon training, DeepONets can be over five orders of magnitude faster than the CFD solver employed to generate the training data and yield good accuracy for unseen Mach numbers within the range of training. Outside this range, DeepONet can still predict accurately and fast if a few sparse measurements are available. We then propose a composite supervised neural network, DeepM&Mnet, that uses multiple pre-trained DeepONets as building blocks and scattered measurements to infer the set of all seven fields in the entire domain of interest. Two DeepM&Mnet architectures are tested, and we demonstrate the accuracy and capacity for efficient data assimilation. DeepM&Mnet is simple and general: it can be employed to construct complex multiphysics and multiscale models and assimilate sparse measurements using pre-trained DeepONets in a “plug-and-play” mode.

在经过正常冲击的高速流动中，流体温度迅速升高，引发下游化学解离反应。化学变化导致流体性质发生明显变化，而这些耦合的多物理场和由此产生的多尺度动力学在数值上具有挑战性。使用传统的计算流体动力学 (CFD) 需要过多的计算成本。在这里，我们提出了一种全新的有效方法，假设状态变量的一些稀疏测量可用，可以无缝集成到模拟算法中。我们采用一种特殊的神经网络来逼近非线性算子，即 DeepONet [23]，它用于在给定来自耦合多物理场系统的其余场的输入的情况下分别预测每个单独的场。我们证明了 DeepONet 对涉及七个场变量的基准高超声速流的有效性。具体来说，我们预测了在高马赫数以及速度和温度场下正常冲击下游的非平衡化学中的五个物种。我们表明，在训练时，DeepONets 可以比用于生成训练数据的 CFD 求解器快五个数量级以上，并在训练范围内对看不见的马赫数产生良好的准确性。在这个范围之外，如果有一些稀疏测量可用，DeepONet 仍然可以准确快速地进行预测。然后，我们提出了一个复合监督神经网络 DeepM&Mnet，它使用多个预训练的 DeepONets 作为构建块和分散的测量值来推断整个感兴趣域中所有七个字段的集合。两个DeepM& Mnet 架构经过测试，我们展示了高效数据同化的准确性和能力。DeepM&Mnet 简单而通用：它可用于构建复杂的多物理场和多尺度模型，并在“即插即用”模式下使用预训练的 DeepONets 来同化稀疏测量。