  The existence or not of pathologies in the context of Lagrangian theory is
studied with the aid of Machine Learning algorithms. Using an example in the
framework of classical mechanics, we make a proof of concept, that the
construction of new physical theories using machine learning is possible.
Specifically, we utilize a fully-connected, feed-forward neural network
architecture, aiming to discriminate between ``healthy'' and ``non-healthy''
Lagrangians, without explicitly extracting the relevant equations of motion.
The network, after training, is used as a fitness function in the concept of a
genetic algorithm and new healthy Lagrangians are constructed. These new
Lagrangians are different from the Lagrangians contained in the initial data
set. Hence, searching for Lagrangians possessing a number of pre-defined
properties is significantly simplified within our approach. The framework
employed in this work can be used to explore more complex physical theories,
such as generalizations of General Relativity in gravitational physics, or
constructions in solid state physics, in which the standard procedure can be
laborious.
