Exoplanet formation inference using conditional invertible neural networks

TL;DR

This work tackles the challenge of quantitatively inferring exoplanet formation parameters from observed planetary properties by using conditional invertible neural networks (cINN) trained on synthetic data from a global planet formation model. By comparing single-planet and multiplanet training scenarios, the study shows that treating planets in multiplanet systems as independent data points yields better sampling of the parameter space and more reliable posterior inferences, while single-planet training tends to yield spurious extrapolations. The results demonstrate that cINN can recover disk parameters for Earth-like planets and reveal correlations among disk properties, suggesting a viable path toward data-driven formation inferences from exoplanet populations. However, achieving robust, system-wide inferences requires larger training datasets and further benchmarking against traditional forward-model surrogates and MCMC approaches.

Abstract

The interpretation of the origin of observed exoplanets is usually done only qualitatively due to uncertainties of key parameters in planet formation models. To allow a quantitative methodology which traces back in time to the planet birth locations, we train recently developed conditional invertible neural networks (cINN) on synthetic data from a global planet formation model which tracks growth from dust grains to evolved final giant planets. In addition to deterministic single planet formation runs, we also include gravitationally interacting planets in multiplanetary systems, which include some measure of chaos. For the latter case, we treat them as individual planets or choose the two or three planets most likely to be discovered by telescopes. We find that training on multiplanetary data, each planet treated as individual point, is promising. The single-planet data only covers a small range of planets and does not extrapolate well to planet properties not included in the training data. Extension to planetary systems will require more training data due to the higher dimensionality of the problem.

Figures (4)

• Figure 1: cINN information flow. Red: forward direction; Purple: inverse; Black: conditions (required for both). Observables $\vec{c}$, planetary mass and semi-major axis, are from the training, test, or real data; model parameters $\vec{x}$ are here $M_{\rm disk}$, $\alpha$, inner edge orbital period, and dust-to-gas ratio.
• Figure 2: Loss function during training and comparison of predicted and training data on the viscous $\alpha$. Left: Validation and training Log Likelihood as a function of training epoch. Center: single-planet histogram on inferred $\alpha$; Right: as Center but for the nominal data. Difference of the posterior mean to training data is normalized by standard deviations as $\sigma = \sqrt{\sigma_{\rm train}^2 + \sigma_{\rm posteriors}^2}$.
• Figure 3: True values against posterior distributions in normalized units for the nominal, single-planet, and 2 detectable planet cases.
• Figure 4: Retrieved and training disk parameters for Earth-analogues. Left: single-planet per disk; Center: nominal, Right: two-planet systems. Training data is shown if both the planet mass and semi-major axis lies within 40% of the Earth (factor 2 of an Earth + Venus system).