NeuralCMS: A deep learning approach to study Jupiter's interior

TL;DR

The paper addresses the challenge of inferring Jupiter's internal structure from the Juno gravity field by accelerating the computationally demanding concentric Maclaurin spheroid forward model with NeuralCMS, a sharing-based DNN surrogate trained on a large CMS dataset. The model achieves predictions of gravity moments and mass within uncertainties comparable to or below current observational errors, enabling rapid exploration of billions of candidate interiors and yielding thousands of plausible structures with only a fraction of CMS computations. Beyond speed, the authors demonstrate interpretability via SHAP, showing core-related parameters strongly influence higher-degree gravity moments and revealing parameter interplay. This approach significantly enhances the practicality of inverse interior modeling for Jupiter and can extend to additional interior features and other gaseous planets, with potential for integration into broader exploration workflows.

Abstract

NASA's Juno mission provided exquisite measurements of Jupiter's gravity field that together with the Galileo entry probe atmospheric measurements constrains the interior structure of the giant planet. Inferring its interior structure range remains a challenging inverse problem requiring a computationally intensive search of combinations of various planetary properties, such as the cloud-level temperature, composition, and core features, requiring the computation of ~10^9 interior models. We propose an efficient deep neural network (DNN) model to generate high-precision wide-ranged interior models based on the very accurate but computationally demanding concentric MacLaurin spheroid (CMS) method. We trained a sharing-based DNN with a large set of CMS results for a four-layer interior model of Jupiter, including a dilute core, to accurately predict the gravity moments and mass, given a combination of interior features. We evaluated the performance of the trained DNN (NeuralCMS) to inspect its predictive limitations. NeuralCMS shows very good performance in predicting the gravity moments, with errors comparable with the uncertainty due to differential rotation, and a very accurate mass prediction. This allowed us to perform a broad parameter space search by computing only ~10^4 actual CMS interior models, resulting in a large sample of plausible interior structures, and reducing the computation time by a factor of 10^5. Moreover, we used a DNN explainability algorithm to analyze the impact of the parameters setting the interior model on the predicted observables, providing information on their nonlinear relation.

Figures (6)

• Figure 1: Schematic view of Jupiter's dilute core model used in this study and the computational process: given a combination of the seven marked interior parameters (left), the CMS method (right) converges to solve the gravity moments and mass, is then compared to the Juno measurements to determine the feasibility. The image in Jupiter's schematic (left) is available at https://www.planetary.org/space-images/merged-cassini-and-juno.
• Figure 2: Schematic diagram of the DNN architecture presented in this study. The hidden layers, both shared and private are marked by dashed black outlines and contain 1024 neurons each. The mass is used for training on the gravity moments $J_{2n}$ and it is predicted separately.
• Figure 3: Performance of NeuralCMS on a sample of $10^4$ models from the validation dataset (a-e). The dashed black lines are the standard deviation of the full validation dataset error $\epsilon_{\sigma}$. The red patch represents the combined uncertainty from dynamics Miguel2022 and measurement errors Durante2020 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. \ref{['eq:loss']} (f).
• Figure 4: Correlation between interior features for the two grid search stages. The black points are model results, and the blue shading is the models' distribution. The left column shows accepted models predicted by NeuralCMS in the first grid search, within the DNN's maximal absolute prediction errors on the validation dataset. In the right column are accepted models computed with CMS found in the second tighter grid search. The axes range is the initial wide search range. The range of $P_{12}$ and $Y_{\rm proto}$ was not reduced. The middle panels nicely reproduce previous results Howard2023a.
• Figure 5: Contribution in ppm to the prediction of $J_6$ of 500 interior models (each point in a row is an individual model) that are consistent with the Juno measurements, within the wind-effect criterion. Higher SHAP values correspond to a larger contribution to the predicted $J_6$. Points are stacked vertically where there is a high density of model solutions. The colors scale the values of each interior parameter. For example, when high, only $Z_1$ positively contributes to $J_6$. The black circles correspond to a specific interior model having the highest SHAP value for $Z_{\rm dilute}$.