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：许多表征物理系统的函数具有加性可分离性。例如，物理学中的力学哈密顿函数、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情形。本研究考虑对函数的代理模型进行加性可分离性测试的场景。检测到代理模型具有加性可分离性后，可利用这一特性改进后续学习过程。因此，具备测试代理模型可分离性的能力具有重要价值。其数学方法在于检验代理模型的混合偏导数是否为零；在实证层面，则是检验该偏导数是否低于某个阈值。我们提出并系统比较了八种计算代理函数混合偏导数的方法，并通过实证研究评估其性能。