A learnable trouble‐cell indicator for hybrid multi‐moment finite‐volume transport modeling on a cubed‐sphere grid

Abstract A novel learnable trouble‐cell indicator embedded seamlessly into the numerical solver is proposed for simulating tracer transport on a cubed‐sphere grid. Unlike most existing machine‐learning‐based trouble‐cell indicators, which are trained separately from numerical solvers, our neural‐network‐based indicator (NNI) is integrated directly into the specific numerical scheme, namely the hybrid multi‐moment (MM) finite‐volume method, which employs a nonlinear reconstruction with a total variation diminishing (TVD) slope limiter, and trained jointly via end‐to‐end simulations of one‐dimensional transport processes. The resulting hybrid multi‐moment transport scheme can achieve fourth‐order accuracy and exact numerical conservation. Numerical benchmark tests on both one‐dimensional and two‐dimensional cubed‐sphere grids demonstrate that the proposed hybrid MM–TVD–NNI scheme achieves sharper profiles near discontinuities and higher overall accuracy than both conventional TVD‐type and weighted essentially non‐oscillatory (WENO)‐type multi‐moment finite‐volume methods using the traditional indicator. In addition, the learnable approach eliminates the need for empirically tuned, problem‐specific parameters, making it more promising for high‐fidelity atmospheric transport simulations. Moreover, the numerical solver embedded within the training framework is not limited to the multi‐moment method and can readily be extended to other existing advanced numerical schemes.