Jannes Papenbrock presents his Semester Thesis on "Augmenting Physical Models with Machine Learning"


The thesis on hand deals with the implementation and investigation of the APHINITY frame-
work proposed by Gallinari et al. [24]. The framework provides an unique decomposition of a
complex dynamical system into a model based part and into an augmenting machine learn-
ing part. While the former part covers the known physics of a system, the latter parts learns
the potentially unknown dynamics. Additionally, the model based part provides an estimation
of the governing physical parameters. Two different APHINITY models are trained with data
obtained from the non-linear, damped pendulum. The model based part of the first APHIN-
ITY model contains the complete dynamics, whereas the other contains only the oscillatory
part. Both are compared to four neural ordinary differential equations. One of these mod-
els incorporates the complete dynamics, another one only the oscillatory part and two in-
corporate different multilayer perceptrons. The APHINITY model with incomplete dynamics
shows a good forecasting capability while also predicting correctly the physical parameter
ω0 governing the oscillation. It outperforms the neural ordinary deferential equation models
with incomplete or no physical knowledge. The forecasting quality of the APHINITY model
with complete dynamics is comparable to the one of the neural ordinary differential equation
model with complete dynamics. Meanwhile, the estimation of the physical parameters made
by the former is better.