Euclidean Distance Degree for Chemical Reaction Networks

In this paper we investigate the complexity of model selection and model testing in chemical reaction networks by formulating them as Euclidean distance problems. We determine closed form expressions for the Euclidean distance degree of the steady state varieties associated to several different families of toric chemical reaction networks with arbitrarily many reaction sites. We show how our results can be used as a metric for the computational cost of solving the model testing and model selection problems.