  We present a machine learning method for model reduction which incorporates
domain-specific physics through candidate functions. Our method estimates an
effective probability distribution and differential equation model from
stochastic simulations of a reaction network. The close connection between
reduced and fine scale descriptions allows approximations derived from the
master equation to be introduced into the learning problem. This representation
is shown to improve generalization and allows a large reduction in network size
for a classic model of inositol trisphosphate (IP3) dependent calcium
oscillations in non-excitable cells.
