Diffusion is an ubiquitous process in nature. Water diffuses in soil when we water our plants. Heat diffuses into a steak when we fry it. And chemical reactants diffuse through the test strip when we take a coronavirus self-test. However, applying diffusion equations from physics often requires simplifying assumptions to estimate unknown factors, such as diffusion rates. Such unknown factors can be learnt from data by physics-aware machine learning and first approaches have generated promising results. However, the mathematics behind current physics-aware machine learning models is mostly incomprehensible to scientists, which hinders knowledge discovery.
*Authors: Matthias Karlbauer, Timothy Praditia, Sebastian Otte, Sergey Oladyshkin, Wolfgang Nowak, Martin V. Butz