In numerical modeling, the advection–diffusion equation describes the long-range transport of atmospheric pollutants. Most numerical models in the atmospheric science community are based on finite difference methods (FDM). In this study, we conduct a comprehensive comparative analysis of standard FDM-based numerical solvers with a deep learning-based solver, the objective of which is to solve the 2D unsteady advection–diffusion equation. The performance is compared on key performance aspects accuracy, stability, and interpolation. In the analysis, we find that despite being trained with a coarse resolution, the DNN solver is the most accurate among all the solvers. For the DNN solver, the mean absolute error and maximum absolute error of fluid concentration are lowered up to 2 orders of magnitude than the FDM-based method, which corresponds to 95% and 97% relative error reduction, respectively. The analysis also shows that the DNN solver is more stable in coarse spatial–temporal domains. Owing to its continuous nature, the DNN can interpolate a solution with consistent accuracy in a resampled spatial and temporal domain magnified up to 5 and 16 times, respectively. This study highlights the fundamental differences in the partial differential equation solving methods by comparing the DNN and FDM-based solvers and presents the DNN solver as a potential alternative to the FDM-based solvers in atmospheric numerical modeling.

在数值模拟中，对流-扩散方程描述了大气污染物的长程迁移。大气科学界的大多数数值模型都基于有限差分法 (FDM)。在这项研究中，我们对基于 FDM 的标准数值求解器与基于深度学习的求解器进行了全面的比较分析，其目的是求解二维非定常对流-扩散方程。性能在关键性能方面的准确性、稳定性和插值上进行比较。在分析中，我们发现尽管使用粗分辨率进行训练，但 DNN 求解器是所有求解器中最准确的。对于 DNN 求解器，流体浓度的平均绝对误差和最大绝对误差比基于 FDM 的方法降低了 2 个数量级，这分别对应于 95% 和 97% 的相对误差减少。分析还表明，DNN 求解器在粗略的时空域中更稳定。由于其连续性，DNN 可以在分别放大 5 倍和 16 倍的重采样时空域中以一致的精度插入解。本研究通过比较 DNN 和基于 FDM 的求解器突出了偏微分方程求解方法的根本差异，并将 DNN 求解器作为大气数值建模中基于 FDM 的求解器的潜在替代方案。DNN 可以在分别放大 5 倍和 16 倍的重采样时空域中以一致的精度插入解。本研究通过比较 DNN 和基于 FDM 的求解器突出了偏微分方程求解方法的根本差异，并将 DNN 求解器作为大气数值建模中基于 FDM 的求解器的潜在替代方案。DNN 可以在分别放大 5 倍和 16 倍的重采样时空域中以一致的精度插入解。本研究通过比较 DNN 和基于 FDM 的求解器突出了偏微分方程求解方法的根本差异，并将 DNN 求解器作为大气数值建模中基于 FDM 的求解器的潜在替代方案。