On Second Order Behaviour in Augmented Neural ODEs: A Short Summary

In Norcliffe et al.[13], we discussed and systematically analysed how Neural ODEs (NODEs) can learn higher-order order dynamics. In particular, we focused on second-order dynamic behaviour and analysed Augmented NODEs (ANODEs), showing that they can learn second-order dynamics with only a few augmented dimensions, but are unable to correctly model the velocity (first derivative). In response, we proposed Second Order NODEs (SONODEs), that build on top of ANODEs, but explicitly take into account the second-order physics-based inductive biases. These biases, besides making them more efficient and noise-robust when modelling second-order dynamics, make them more interpretable than ANODEs, therefore more suitable in many real-world scientific modelling applications.