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.

翻译：近年来，基于深度神经网络（DNN）的代理模型已被广泛用于求解传统上通过数值模拟处理的偏微分方程。然而，这类代理模型侧重于训练数据集的全局插值，因此需要庞大的网络结构。该过程既耗时又计算成本高昂，从而限制了其在复杂物理问题高保真预测中的应用。本研究提出了一种局部收敛输入的神经网络（NNLCI），用于基于非结构化数据的高保真预测。该框架利用依赖局部域与收敛粗解作为输入，大幅降低了计算资源和训练时间。作为验证案例，NNLCI方法被应用于研究带有凸块的通道内无粘超声速流动。通过考虑不同的凸块几何形状和位置，对所提方法的有效性和多功能性进行了基准测试。包括激波相互作用在内的详细流动结构被系统地进行了分析。