Using Deep Neural Networks to compute the mass of forming planets

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. We developed a method 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,(ISM and reduced). 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.Comment: accepted in A&A. Animations visible at http://nccr-planets.ch/research/phase2/domain2/project5/machine-learning-and-advanced-statistical-analysis/ and code available at https://github.com/yalibert/DNN_internal_structur

Organizational Learning in Schools Pursuing Social Justice: Fostering Educational Entrepreneurship and Boundary Spanning

The field of socially just educational leadership is focused on promoting improve· ments in the teaching and learning environment as demonstrated by student learning gains, particularly for traditionally marginalized students. The field has identified priorities (i.e., school improvement, democratic community, and social justice) and steps to pursue these priorities (specific strategies school leaders can take and conditions they can foster). Building on this literature, this article exam· ines organizational learning in school communities that claim to be pursuing these priorities. It argues that organizational learning is a lens for socially just educational leaders to link theory with practice and to shift their focus from the knowledge, skills, and dispositions of individuals to the communities of practice within schools. It first describes a theoretical framework for examining organi· zational learning in schools, then analyzes two school settings illustrating orga· nizational learning in educational entrepreneurship and boundary spanning. It concludes with a discussion of the implications this has for the broader field of socially just educational leadership