Dynamical models from data, including constants of motion

The FJet method is introduced for modeling a dynamical system from data; it is based on using machine learning to model the updates of the phase space variables. Excellent agreement is found, using examples which have damping and external forcing. The underlying differential equation is also accurately determined. An analogy with the Runge-Kutta scheme provides insights into the function space and error estimates. Constants of motion can be numerically determined by combining FJet and Lie symmetry techniques; this can be done for both conservative and dissipative dynamics, and is demonstrated.