  In this work we present new scalable, information theory-based variational
methods for the efficient model reduction of high-dimensional deterministic and
stochastic reaction networks. The proposed methodology combines, (a)
information theoretic tools for sensitivity analysis that allow us to identify
the proper coarse variables of the reaction network, with (b) variational
approximate inference methods for training a best-fit reduced model. This
approach takes advantage of both physicochemical modeling and data-based
approaches and allows to construct optimal parameterized reduced dynamics in
the number of variables, reactions and parameters, while controlling the
information loss due to the reduction. We demonstrate the effectiveness of our
model reduction method on several complex, high-dimensional chemical reaction
networks arising in biochemistry.
