Many functions characterising physical systems are additively separable. This is the case, for instance, of mechanical Hamiltonian functions in physics, population growth equations in biology, and consumer preference and utility functions in economics. We consider the scenario in which a surrogate of a function is to be tested for additive separability. The detection that the surrogate is additively separable can be leveraged to improve further learning. Hence, it is beneficial to have the ability to test for such separability in surrogates. The mathematical approach is to test if the mixed partial derivative of the surrogate is zero; or empirically, lower than a threshold. We present and comparatively and empirically evaluate the eight methods to compute the mixed partial derivative of a surrogate function.

翻译：许多描述物理系统的函数具有加性可分离性。例如，物理学中的机械哈密顿函数、生物学中的种群增长方程以及经济学中的消费者偏好与效用函数均属此类。我们考虑对函数代理模型进行加性可分离性测试的场景。若检测到代理模型具有加性可分离性，则可利用该特性改进后续学习过程。因此，具备对代理模型进行此类可分离性测试的能力具有重要意义。数学方法需检验代理模型的混合偏导数是否为零；工程实践中则检验其是否低于某一阈值。本文对八种计算代理模型混合偏导数的方法进行了系统性的比较与实证评估。