The immense computational cost of traditional numerical weather and climate
models has sparked the development of machine learning (ML) based emulators.
Because ML methods benefit from long records of training data, it is common to
use datasets that are temporally subsampled relative to the time steps required
for the numerical integration of differential equations. Here, we investigate
how this often overlooked processing step affects the quality of an emulator's
predictions. We implement two ML architectures from a class of methods called
reservoir computing: (1) a form of Nonlinear Vector Autoregression (NVAR), and
(2) an Echo State Network (ESN). Despite their simplicity, it is well
documented that these architectures excel at predicting low dimensional chaotic
dynamics. We are therefore motivated to test these architectures in an
idealized setting of predicting high dimensional geophysical turbulence as
represented by Surface Quasi-Geostrophic dynamics. In all cases, subsampling
the training data consistently leads to an increased bias at small spatial
scales that resembles numerical diffusion. Interestingly, the NVAR architecture
becomes unstable when the temporal resolution is increased, indicating that the
polynomial based interactions are insufficient at capturing the detailed
nonlinearities of the turbulent flow. The ESN architecture is found to be more
robust, suggesting a benefit to the more expensive but more general structure.
Spectral errors are reduced by including a penalty on the kinetic energy
density spectrum during training, although the subsampling related errors
persist. Future work is warranted to understand how the temporal resolution of
training data affects other ML architectures.

该论文研究了机器学习方法在模拟高维地球物理湍流过程中的预测性能，并发现训练数据的时间分辨率对于预测性能的影响。