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 (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.

中文翻译：

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多元有理逼近的实用算法

摘要 我们提出了两种计算多元函数有理近似的方法，其动机是它们作为高能物理 (HEP) 应用的替代模型的有效性。我们的第一种方法建立在 Stieltjes 过程的基础上，以有效且稳健地计算有理近似的系数。我们的第二种方法基于优化公式，该公式允许我们在有理近似中包含结构约束（特别是要求不存在奇点的约束），从而产生我们使用外近似方法解决的半无限优化问题。我们展示了合成和真实 HEP 数据的结果，并将我们的方法的近似质量与传统多项式近似的质量进行了比较。