  In recent years, surrogate models based on deep neural networks (DNN) have
been widely used to solve partial differential equations, which were
traditionally handled by means of numerical simulations. This kind of surrogate
models, however, focuses on global interpolation of the training dataset, and
thus requires a large network structure. The process is both time consuming and
computationally costly, thereby restricting their use for high-fidelity
prediction of complex physical problems. In the present study, we develop a
neural network with local converging input (NNLCI) for high-fidelity prediction
using unstructured data. The framework utilizes the local domain of dependence
with converging coarse solutions as input, which greatly reduces computational
resource and training time. As a validation case, the NNLCI method is applied
to study inviscid supersonic flows in channels with bumps. Different bump
geometries and locations are considered to benchmark the effectiveness and
versability of the proposed approach. Detailed flow structures, including
shock-wave interactions, are examined systematically.
