We present a taxonomy of research on Machine Learning (ML) applied to enhance simulations together with a catalog of some activities. We cover eight patterns for the link of ML to the simulations or systems plus three algorithmic areas: particle dynamics, agent-based models and partial differential equations. The patterns are further divided into three action areas: Improving simulation with Configurations and Integration of Data, Learn Structure, Theory and Model for Simulation, and Learn to make Surrogates.

We recently outlined the vision of "Learning Everywhere" which captures the possibility and impact of how learning methods and traditional HPC methods can be coupled together. A primary driver of such coupling is the promise that Machine Learning (ML) will give major performance improvements for traditional HPC simulations. Motivated by this potential, the ML around HPC class of integration is of particular significance. In a related follow-up paper, we provided an initial taxonomy for integrating learning around HPC methods. In this paper, which is part of the Learning Everywhere series, we discuss "how" learning methods and HPC simulations are being integrated to enhance effective performance of computations. This paper identifies several modes --- substitution, assimilation, and control, in which learning methods integrate with HPC simulations and provide representative applications in each mode. This paper discusses some open research questions and we hope will motivate and clear the ground for MLaroundHPC benchmarks.