# A Comparative Evaluation of Additive Separability Tests for Physics-Informed Machine Learning

arXiv: https://arxiv.org/abs/2312.09775 · HTML: https://mlsanity.com/paper/2312.09775/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 25 references that are in the map.
- First posted on arXiv 15 Dec 2023.

## Builds on (most cited first, 7 of 7)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Deconstructing the Inductive Biases of Hamiltonian Neural Networks](https://mlsanity.com/paper/2202.04836/) (2022)
- [Compositional Modeling of Nonlinear Dynamical Systems with ODE-based Random Features](https://mlsanity.com/paper/2106.05960/) (2021)
- [ModLaNets: Learning Generalisable Dynamics via Modularity and Physical Inductive Bias](https://mlsanity.com/paper/2206.12325/) (2022)
- [What's Next? Predicting Hamiltonian Dynamics from Discrete Observations of a Vector Field](https://mlsanity.com/paper/2312.08944/) (2023)

## Abstract (arXiv)

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.