  We present the interpretable meta neural ordinary differential equation
(iMODE) method to rapidly learn generalizable (i.e., not parameter-specific)
dynamics from trajectories of multiple dynamical systems that vary in their
physical parameters. The iMODE method learns meta-knowledge, the functional
variations of the force field of dynamical system instances without knowing the
physical parameters, by adopting a bi-level optimization framework: an outer
level capturing the common force field form among studied dynamical system
instances and an inner level adapting to individual system instances. A priori
physical knowledge can be conveniently embedded in the neural network
architecture as inductive bias, such as conservative force field and Euclidean
symmetry. With the learned meta-knowledge, iMODE can model an unseen system
within seconds, and inversely reveal knowledge on the physical parameters of a
system, or as a Neural Gauge to "measure" the physical parameters of an unseen
system with observed trajectories. We test the validity of the iMODE method on
bistable, double pendulum, Van der Pol, Slinky, and reaction-diffusion systems.
