Performance of NeuralCMS on a sample of 10⁴ models from the validation dataset (a–e). The dashed black lines are the standard deviation of the full validation dataset error ϵ_σ. The red patch represents the combined uncertainty from dynamics (Miguel et al. 2022) and measurement errors (Durante et al. 2020) for the gravity harmonics: $\sqrt{{(3{\sigma }_{\mathrm{wind}})}^2+{(3{\sigma }_{\mathrm{Juno}})}^2}$. The mass uncertainty is due to various G values. The learning curve of the DNN at every ten epochs using Eq. (1) (f).