Grid-based exoplanet atmospheric mass loss predictions through neural network

TL;DR

This work tackles the challenge of quickly estimating exoplanet atmospheric mass-loss rates by learning from a large grid of hydrodynamic upper-atmosphere models. It introduces MLink, a dense neural network-based interpolator, and demonstrates its superior interpolation accuracy across a six-dimensional parameter space compared with traditional linear and radial-basis schemes. Validation on a substantial test set shows that MLink reduces errors, especially near grid edges and regime transitions, and yields evolutionary tracks similar to other ML methods while mitigating biases. The approach enables rapid exploration of larger, more complex model grids incorporating additional physics, with practical implications for interpreting planetary radii distributions and evolution.

Abstract

The fast and accurate estimation of planetary mass-loss rates is critical for planet population and evolution modelling. We use machine learning (ML) for fast interpolation across an existing large grid of hydrodynamic upper atmosphere models, providing mass-loss rates for any planet inside the grid boundaries with superior accuracy compared to previously published interpolation schemes. We consider an already available grid comprising about 11000 hydrodynamic upper atmosphere models for training and generate an additional grid of about 250 models for testing purposes. We develop the ML interpolation scheme (dubbed "atmospheric Mass Loss INquiry frameworK"; MLink) using a Dense Neural Network, further comparing the results with what was obtained employing classical approaches (e.g. linear interpolation and radial basis function-based regression). Finally, we study the impact of the different interpolation schemes on the evolution of a small sample of carefully selected synthetic planets. MLink provides high-quality interpolation across the entire parameter space by significantly reducing both the number of points with large interpolation errors and the maximum interpolation error compared to previously available schemes. For most cases, evolutionary tracks computed employing MLink and classical schemes lead to comparable planetary parameters at Gyr-timescales. However, particularly for planets close to the top edge of the radius gap, the difference between the predicted planetary radii at a given age of tracks obtained employing MLink and classical interpolation schemes can exceed the typical observational uncertainties. Machine learning can be successfully used to estimate atmospheric mass-loss rates from model grids paving the way to explore future larger and more complex grids of models computed accounting for more physical processes.

Figures (14)

• Figure 1: Illustration of the criteria setting the additional boundaries on the grid (see Section \ref{['sec::grid_structure']}) in the $M_{\rm pl}$--$T_{\rm eq}$ plane for $5\,R_{\oplus}$ (top) and $10\,R_{\oplus}$ (bottom) planets. The orange, blue, yellow, green, and violet dashed lines marked as $R_{\rm RB}(M_*)$ show the upper $T_{\rm eq}$($M_{\rm pl}$) boundaries set by criterion II ($R_{\rm roche}\,\geq\,1.2R_{\rm pl}$) for planets orbiting 0.4, 0.6, 0.8, 1.0, and 1.3 $M_{\odot}$ stars, respectively. The solid line contours of the respective colours show the grid ranges in the $T_{\rm eq}$--$M_{\rm pl}$ plane for each of the stellar masses, with all areas sharing the same lower boundary controlled by criterion III (black dashed line for $\Lambda\,=\,80$; black dotted line for $\Lambda\,=\,160$). In the bottom panel, the region on the left of the shaded area (grid ranges) is excluded by the low-density criterion I ($\rho\geq0.03$ g cm$^{-3}$; black dash-dotted line).
• Figure 2: Atmospheric mass-loss rates predicted by the hydrodynamic model for planets with $R_{\rm pl}\,=\,5\,R_{\oplus}$ and $M_{\rm pl}$ between 1 $M_{\oplus}$ and 108.6 $M_{\oplus}$ orbiting a $0.6\,M_{\odot}$ star at an orbital separation corresponding to $T_{\rm eq}$ values of 300 K (blue circles), 700 K (green circles), 1100 K (deep yellow circles), 1500 K (violet circles), and 2000 K (red circles) as a function of $M_{\rm pl}$ (top), $\Lambda$ (middle), and $\Lambda\times K$ (bottom). Lines of different styles indicate the mass-loss rates predicted by the energy-limited approximation $\dot{M}_{\rm EL}$ (dash-dotted), core-powered mass loss $\dot{M}_{\rm CP}$ (solid), and Roche lobe overflow $\dot{M}_{\rm RL}$ (dashed), with the colour of the lines following the same scheme as that of the circles. For $\dot{M}_{\rm EL}$, we considered the same EUV fluxes as for the hydrodynamic models shown in the plots, namely 3.0 $\rm erg\,s\,cm^{-2}$ for the orbital separation corresponding to $T_{\rm eq}$ of 300 K, 89.1 $\rm erg\,s\,cm^{-2}$ for 700 K, 543.3 $\rm erg\,s\,cm^{-2}$ for 1100 K, 1878.6 $\rm erg\,s\,cm^{-2}$ for 1500 K, and 5937.3 $\rm erg\,s\,cm^{-2}$ for 2000 K.
• Figure 3: Position of the planets comprising the test dataset in the $M_*$--$T_{\rm eq}$ plane (top), in the $a$--$F_{\rm EUV}$ plane (middle), and in the $M_{\rm pl}$--$R_{\rm pl}$ plane (bottom). In each panel, points are colour-coded according to the value of $\Lambda\times K$ (see the scale in the top panel).
• Figure 4: Definition of the location of the regime transition point ($\Lambda_{\rm RTP}$) for $M_*\,=\,0.6$$M_{\odot}$, $T_{\rm eq}\,=\,1100$ K, $R_{\rm pl}\,=\,5$$R_{\oplus}$, and $F_{\rm EUV}\,=\,543.3$$\rm erg\,s\,cm^{-2}$. Grey circles show the atmospheric mass loss rates against $\Lambda$ given by the hydrodynamic model. The red asterisks denote points identified as planets in the core-powered or Roche lobe overflow regime ($\dot{M}\geq10^{12}$ g s$^{-1}$ and $R_{\rm roche}>1.5$; the latter condition excludes points that are too much affected by the lower boundary condition). The blue crosses denote the points in the XUV-driven regime ($\dot{M}\leq10^9$ g s$^{-1}$). The red and the blue dashed lines show the linear fits in the $\log{\dot{M}}$--$\log{\Lambda}$ space for these two groups of points, as specified in the plot. The yellow star gives the position of the regime transition point.
• Figure 5: Ratio of the mass-loss rates predicted for the test planets by interpol2021 (panels a and c) and interpol2024 (panels b and d) to the true values given by the hydrodynamic model, against $\Lambda$ and $\Lambda\times K$, respectively. The points are colour-coded according to the $J_{\rm bord}$ value. In panels (c) and (d), the red points have $J_{\rm trans}\,=\,1$, while the red points marked by a yellow plus are those with $J_{\rm trans}\,=\,2$. For reference, the two horizontal black lines in each panel lie at 0.5 and 2.