Multivariate Rational Approximation

TL;DR

This paper introduces two novel methods for multivariate rational approximation, enhancing surrogate modeling in high-energy physics by improving efficiency, robustness, and the ability to incorporate structural constraints.

Contribution

It proposes a Stieltjes process-based method and an optimization-based approach for multivariate rational approximation, including structural constraints, with demonstrated effectiveness on HEP data.

Findings

The Stieltjes process method efficiently computes rational coefficients.

The optimization approach allows structural constraints in approximations.

Our methods outperform traditional polynomial approximations in HEP applications.

Abstract

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.