  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, 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 by predicting 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.
