  We present two approaches for computing rational approximations to
multivariate functions, motivated by their effectiveness as surrogate models
for high-energy physics (HEP) applications. Our first approach builds on the
Stieltjes process to efficiently and robustly compute the coefficients of the
rational approximation. Our second approach is based on an optimization
formulation that allows us to include structural constraints on the rational
approximation, resulting in a semi-infinite optimization problem that we solve
using an outer approximation approach. We present results for synthetic and
real-life HEP data, and we compare the approximation quality of our approaches
with that of traditional polynomial approximations.
