Metalearning generalizable dynamics from trajectories

TL;DR

The paper introduces iMODE, an interpretable meta neural ODE approach that rapidly learns generalizable dynamics from multiple trajectories, enabling quick modeling of unseen systems and inference of physical parameters.

Contribution

The novel iMODE method learns meta-knowledge of dynamical systems without physical parameters, using bi-level optimization and physical priors, for fast generalization and parameter inference.

Findings

iMODE models unseen systems within seconds

It reveals physical parameters from trajectories

Effective on diverse dynamical systems

Abstract

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.