17 USC 105 interim-entered record; under review.The article of record as published may be found at https://doi.org/10.1016/j.cpc.2020.107663We 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 (in particular, constraints demanding
the absence of singularities), 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.This work was supported by the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research, under Contract DE-AC02-06CH11357. Support for this work was provided through the SciDAC program funded by U.S. Department of Energy, Office of Science, Advanced Scientific Computing Re search. This work was also supported by the U.S. Department of Energy through grant DE-FG02-05ER25694, and by Fermi Re search Alliance, LLC, United States of America under Contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics. This work was supported in part by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research and Office of Nuclear Physics, Scientific Discovery through Advanced Computing (SciDAC) program through the FASTMath Institute under Contract No. DE-AC02-05CH11231 at Lawrence Berkeley National Laboratory
