A Comparative Evaluation of Additive Separability Tests for Physics-Informed Machine Learning
This work addresses the need for efficient separability detection in surrogates for applications in physics, biology, and economics, but it is incremental as it focuses on comparative evaluation of existing methods.
The paper tackles the problem of testing surrogate functions for additive separability, which can improve learning in physics-informed machine learning, by empirically evaluating eight methods to compute mixed partial derivatives.
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.