“…With regards to the satisfaction of physical constraints, the previous studies (Krasnopolsky et al, 2010;Lagerquist et al, 2021;Liu et al, 2020;Roh & Song, 2020) trained NN-based emulators to output profiles of heating rates and fluxes at the surface and top-of-atmosphere directly, which causes the issues with energy conservation. Cachay et al (2021) and Ukkonen (2022) chose to predict the radiative fluxes and compute heating rates from fluxes, which ensures physical consistency (Yuval et al, 2021). However, Ukkonen (2022) found that the heating rates are highly sensitive to the continuity in the fluxes profile, and small errors of fluxes lead to relatively large errors in heating rates.…”