Machine learning and serving of discrete field theories

Area of Science:

• Physics
• Computer Science
• Machine Learning

Background:

• Traditional methods for learning physical theories often struggle with continuous theories.
• Existing algorithms for solving differential equations can be less efficient than structure-preserving methods.

Purpose of the Study:

• To develop a novel machine learning approach for creating and utilizing discrete field theories.
• To overcome the challenges of applying AI to continuous physical theories.
• To demonstrate the effectiveness of the proposed algorithms in predicting physical phenomena.

Main Methods:

• A learning algorithm trains discrete field theories from observational data on a spacetime lattice.
• A serving algorithm uses learned theories to predict new observations under different conditions.
• The serving algorithm employs structure-preserving geometric methods, outperforming conventional discretization techniques.

Main Results:

• The method successfully learns discrete field theories from observational data.
• The serving algorithm accurately predicts diverse planetary orbits, including escaping trajectories, without prior knowledge of Newtonian physics.
• Effectiveness demonstrated through nonlinear oscillations and the Kepler problem.

Conclusions:

• The developed machine learning method provides an effective way to learn and serve discrete field theories.
• This approach offers advantages over traditional methods, particularly for complex physical systems.
• The algorithms show potential for applications involving special and general relativity.