Multiscale stochastic parameterization with deep Mori-Zwanzig formalism

We propose a deep learning implementation of the Mori-Zwanzig formalism, termed DMZ, as a principled multiscale, memory-aware, and stochastic modeling framework for developing subgrid-scale parameterization schemes in global circulation model. Here, robust multiscale representations are needed for stable and skillful long-term forecasts but remain limited by computational capacity. Coupled online tests with DMZ-based parameterization demonstrate stable multiyear simulation runs that maintain physically consistent interannual variability. When evaluated against satellite observations, DMZ significantly reduces precipitation bias, particularly over the Pacific Ocean where dominant modes of variability such as El Niño-Southern Oscillation emerge. These results highlight DMZ as a promising modeling paradigm that provides a principled stochastic, memory-based parameterization scheme to improve the fidelity of Earth system simulations.