Three-dimensional (3D) multiphysics models are powerful tools for investigating the distributions of physical quantities such as temperature inside solid oxide cell (SOC) stacks, but their high computational cost remains an obstacle to their application in simulating industrial-scale stacks with tens of cells. To accelerate the simulation for the 3D model of a novel flat-chip SOC (FCSOC) stack, this study proposes a simplification method that replaces part of the governing equations with data-driven surrogate cell submodels. The submodels, built with the adaptive polynomial approximation (APA) method, take the form of polynomials and are easy to integrate into commercial CFD software such as COMSOL. Simulation shows that the simplified stack model can predict the temperatures and voltages accurately compared with the original stack model. At the same time, the time and memory required for computation are reduced by approximately 60% for a short stack model containing seven cells, owing to the simplified fuel-side mass transfer and charge transfer processes. For a large stack model with 21 cells, the reduction in computation time can even exceed 70%. The reduced computational cost makes it possible to simulate the models of industrial-scale FCSOC stacks with up to 61 cells.