Accurate and thermodynamically consistent hydrogen equation of state for planetary modeling with flow matching

Accurate determination of the equation of state of dense hydrogen is essential for understanding gas giants. Currently, there is still no consensus on methods for calculating its entropy, which play a fundamental role and can result in qualitatively different predictions for Jupiter's interior. Here, we investigate various aspects of entropy calculation for dense hydrogen based on ab initio molecular dynamics simulations. Specifically, we employ the recently developed flow matching method to validate the accuracy of the traditional thermodynamic integration approach. We then clearly identify pitfalls in previous attempts and propose a reliable framework for constructing the hydrogen equation of state, which is accurate and thermodynamically consistent across a wide range of temperature and pressure conditions. This allows us to conclusively address the long-standing discrepancies in Jupiter's adiabat among earlier studies, demonstrating the potential of our approach for providing reliable equations of state of diverse materials.

Characterizing Jupiter's interior using machine learning reveals four key structures

The internal structure of Jupiter is constrained by the precise gravity field measurements by NASA's Juno mission, atmospheric data from the Galileo entry probe, and Voyager radio occultations. Not only are these observations few compared to the possible interior setups and their multiple controlling parameters, but they remain challenging to reconcile. As a complex, multidimensional problem, characterizing typical structures can help simplify the modeling process. We used NeuralCMS, a deep learning model based on the accurate concentric Maclaurin spheroid (CMS) method, coupled with a fully consistent wind model to efficiently explore a wide range of interior models without prior assumptions. We then identified those consistent with the measurements and clustered the plausible combinations of parameters controlling the interior. We determine the plausible ranges of internal structures and the dynamical contributions to Jupiter's gravity field. Four typical interior structures are identified, characterized by their envelope and core properties. This reduces the dimensionality of Jupiter's interior to only two effective parameters. Within the reduced 2D phase space, we show that the most observationally constrained structures fall within one of the key structures, but they require a higher 1 bar temperature than the observed value. We provide a robust framework for characterizing giant planet interiors with consistent wind treatment, demonstrating that for Jupiter, wind constraints strongly impact the gravity harmonics while the interior parameter distribution remains largely unchanged. Importantly, we find that Jupiter's interior can be described by two effective parameters that clearly distinguish the four characteristic structures and conclude that atmospheric measurements may not fully represent the entire envelope.

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

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.