| Abstract | We begin the lecture with some general discussion of the informative and intelligent scientific computing paradigm. Then we give an illustration via the mathematical problem of learning unknown dynamics from observation data. When the underlying dynamic model is discretized in time by linear multistep methods, the conventional theory of consistency, stability and convergence theory for time integration must be reexamined for dynamics discovery. Refined criteria are proposed as part of a new numerical analysis framework to assure stable and convergent discovery of dynamics in some idealized settings, which may offer guidance to more practical applications. |
