J/A+A/626/A21 DNN internal structure code (Alibert+, 2019)
Using deep neural networks to compute the mass of forming planets.
Alibert Y., Venturini J.
<Astron. Astrophys. 626, A21 (2019)>
=2019A&A...626A..21A 2019A&A...626A..21A (SIMBAD/NED BibCode)
ADC_Keywords: Models
Keywords: planetary systems - planets and satellites: formation -
Abstract:
Computing the mass of planetary envelopes and the critical mass beyond
which planets accrete gas in a runaway fashion is important when
studying planet formation, in particular for planets up to the Neptune
mass range. This computation requires in principle solving a set of
differential equations, the internal structure equations, for some
boundary conditions (pressure, temperature in the protoplanetary disk
where a planet forms, core mass and accretion rate of solids by the
planet). Solving these equations in turn proves being time consuming
and sometimes numerically unstable.
The aim is to provide a way to approximate the result of integrating
the internal structure equations for a variety of boundary conditions.
We compute a set of planet internal structures for a very large number
(millions) of boundary conditions, considering two opacities, namely
the ISM one and a reduced one. This database is then used to train
Deep Neural Networks in order to predict the critical core mass as
well as the mass of planetary envelopes as a function of the boundary
conditions.
We show that our neural networks provide a very good approximation (at
the level of percents) of the result obtained by solving interior
structure equations, but with a much smaller required computer time.
The difference with the real solution is much smaller than the one
obtained using some analytical formulas available in the literature
which at best only provide the correct order of magnitude. We compare
the results of the DNN with other popular machine learning methods
(Random Forest, Gradient Boost, Support Vector Regression) and show
that the DNN outperforms these methods by a factor of at least two.
We show that some analytical formulas that can be found in various
papers can severely overestimate the mass of planets, therefore
predicting the formation of planets in the Jupiter-mass regime instead
of the Neptune-mass regime. The python tools that we provide allow to
compute the critical mass and the mass of planetary envelopes in a
variety of cases, without having to solve the internal structure
equations. These tools can easily replace the aforementioned
analytical formulas, while providing much more accurate results.
Description:
We trained Deep Neural Networks to compute the critical core mass and
envelope masses of forming planets, for a variety of conditions
(formation location, temperature and pressure in the disc, core mass,
solid accretion rate). The resulting DNNs, which can be easily
implemented with the tools we provide on github
(https://github.com/yalibert/DNN_ internal_structure/), give very
similar results to the ones obtained by solving the internal structure
equations, using a much reduced computer time.
File Summary:
--------------------------------------------------------------------------------
FileName Lrecl Records Explanations
--------------------------------------------------------------------------------
ReadMe 80 . This file
DNNcode.tar 512 7300 DNN internal structure code
--------------------------------------------------------------------------------
Acknowledgements:
Yann Alibert, yann.alibert(at)space.unibe.ch
(End) Patricia Vannier [CDS] 29-Mar-2019