Main challenges when using machine learning to “model” physics systems

• Machine learning may violate conservation laws
• Machine learning may not focus on the physically meaningful variable
• Machine learning may provide a solution difficult to be interpreted

None of these is specifically connected with machine learning

Machine learning may violate conservation laws: Numerical integration of ordinary differential equation can also lead to violation of conservation laws, e.g. energy

Machine learning may not focus on the physically meaningful variable: This is a general challenge in describing any physical system, when the right variables are considered, often the solution can be “guessed” by dimensional analysis (Buckingham Pi Theorem)

Machine learning may provide a solution difficult to be interpreted: Using standard tools, like orthogonal basis functions that do not respect the symmetries of the problem also will lead to series expansion without direct physical meaning