Neural Infalling Cloud Equations (NICE): Increasing the Efficacy of Subgrid Models and Scientific Equation Discovery using Neural ODEs and Symbolic Regression

It is now well established that galactic systems are inherently multiphase, and that understanding the roles and interactions of the various phases is key towards a more complete picture of galaxy formation and evolution. For example, these interactions play a pivotal role in the cycling of baryons which fuels star formation. It remains a challenge that the transport and dynamics of cold clouds in their surrounding hot environment are governed by complex small scale processes (such as the interplay of turbulence and radiative cooling) that determine how the phases exchange mass, momentum and energy. Large scale models thus require subgrid prescriptions in the form of models validated on small scale simulations, which can take the form of a system of coupled differential equations. In this work, we explore using neural ordinary differential equations which embed a neural network as a term in the subgrid model to capture an uncertain physical process. We then apply Symbolic Regression on the learned model to potentially discover new insights into the physics of cloud-environment interactions. We test this on both generated mock data and actual simulation data. We also extend the neural ODE to include a secondary neural term. We show that neural ODEs in tandem with Symbolic Regression can be used to enhance the accuracy and efficiency of subgrid models, and/or discover the underlying equations to improve generality and scientific understanding. We highlight the potential of this scientific machine learning approach as a natural extension to the traditional modelling paradigm, both for the development of semi-analytic models and for physically interpretable equation discovery in complex non-linear systems.