Artifacts of Numerical Integration in Learning Dynamical Systems
The analysis investigates how using a numerical integrator to approximate system flow creates artifacts in learning dynamics. It found that the stability region of the chosen integrator directly distorts what is learned, potentially causing damped systems to be misidentified as having 'anti-damping' or reversed oscillation directions. The paper recommends the Implicit Midpoint Rule as a principled default choice due to its stable region.