Building healthy Lagrangian theories with machine learning
Abstract
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 fullyconnected, feedforward neural network architecture, aiming to discriminate between “healthy” and “nonhealthy” 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 predefined 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.
 Publication:

International Journal of Modern Physics D
 Pub Date:
 2021
 DOI:
 10.1142/S0218271821500851
 arXiv:
 arXiv:2002.00049
 Bibcode:
 2021IJMPD..3050085V
 Keywords:

 Machine learning;
 Lagrangians;
 neural networks;
 higherderivatives;
 modified gravity;
 04.50.Kd;
 98.80.−k;
 95.36.+x;
 98.80.Es;
 Modified theories of gravity;
 Dark energy;
 Observational cosmology;
 Physics  Computational Physics;
 General Relativity and Quantum Cosmology
 EPrint:
 10 pages, 4 figures, 5 tables, version to appear in Int.J.Mod.Phys.D