Neural infalling cloud equations (NICE): increasing the efficacy of subgrid models and scientific equation discovery using neural ODEs and symbolic regression

Galactic systems are inherently multiphase, and understanding the roles and interactions of the various phases is key towards a more complete picture of galaxy formation and evolution. For instance, these interactions play a pivotal role in the cycling of baryons which fuels star formation. 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 often take the form of coupled differential equations. In this work, we explore using neural ordinary differential equations (ODEs) which embed neural networks as terms in the model to capture an uncertain physical process. We then apply symbolic regression 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-analytical models and for physically interpretable equation discovery in complex non-linear systems.