Metalearning Generalizable Dynamics from Trajectories

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 metaknowledge, the functional variations of the force field of dynamical system instances without knowing the physical parameters, by adopting a bilevel 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 metaknowledge, 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. iMODE can be generally applied to a dynamical system of an arbitrary type or number of physical parameters and is validated on bistable, double pendulum, Van der Pol, Slinky, and reaction-diffusion systems.