Downscaling using CDAnet under observational and model noise: the Rayleigh-Bénard convection paradigm

Efficient downscaling of large ensembles of coarse-scale information is crucial in several applications, such as oceanic and atmospheric modeling. The determining form map is a theoretical lifting function from the low-resolution solution trajectories of a dissipative dynamical system to their corresponding high-resolution counterparts. Recently, a physics-informed deep neural network (“CDAnet”) was introduced, providing a surrogate of the determining form map for efficient downscaling. CDAnet was demonstrated to efficiently downscale noise-free coarse-scale data in a deterministic setting. Herein, the performance of well-trained CDAnet models is analyzed in a stochastic setting involving (i) observational noise, (ii) model noise, and (iii) a combination of observational and model noise. The analysis is performed employing the Rayleigh-Bénard convection paradigm, under three training conditions, namely, training with perfect, noisy, or downscaled data. Furthermore, the effects of noise, Rayleigh number, and spatial and temporal resolutions of the input coarse-scale information on the downscaled fields are examined. The results suggest that the expected $$\ell _2$$ -error of CDAnet behaves quadratically in terms of the standard deviations of the observational and model noise. The results also suggest that CDAnet responds to uncertainties similar to the theorized and numerically-validated CDA behavior with an additional error overhead due to CDAnet being a surrogate of the determining form map.