Georgia Institute of Technology College of Sciences

Deep neural network–based surrogate models have recently gained traction for solving fluid-flow partial differential equations, but their reliance on global interpolation often demands large, computationally expensive architectures and extensive training data. Neural networks with local converging inputs (NNLCI) offer a contrasting strategy. By restricting attention to the local domain of dependence and using converging coarse-grid solutions as inputs, NNLCI dramatically reduces computational cost and data requirements while achieving strong generalization. In this work, we extend the NNLCI framework to the three‑dimensional Stokes equations and introduce a new subdomain data generation methodology specifically tailored for NNLCI, enabling high‑fidelity prediction while completely eliminating the need to compute fine‑grid numerical solutions on the full domain at any stage of the computing process. This innovation eliminates the most computationally intensive component of 3D simulations at its root.