In Sect. VII, we introduce the class of MSMs tailored on stochastic Stuart-Landau oscillators, aimed at the modeling of the aforementioned reduction coordinates corresponding here to the projection of the dataset onto the DAH modes; see Sectns. VII A and VII B. These elemental models-the multilayer Stuart-Landau models (MSLMs)-are stacked per frequency, only coupled at different frequencies by the same noise realization; see Sect. VII C. In Sect. VIII, we finally show the flexibility of the DAH-MSLM modeling approach, by its ability to provide skilled stochastic inverse models for **data** issued either from the nonlinear chaotic Lorenz 96 model, or a stochastic heat equation driven by a space-time white noise. Concluding remarks discuss then in Sect. IX directions for future research.