Metalearning Generalizable Dynamics from Trajectories.

Area of Science:

• Computational Physics
• Machine Learning
• Dynamical Systems Theory

Background:

• Learning dynamics from observational data is crucial for understanding complex systems.
• Existing methods often struggle with generalizability across systems with varying physical parameters.
• Parameter-specific models require extensive retraining for new system configurations.

Purpose of the Study:

• To introduce a novel method, interpretable meta neural ordinary differential equation (iMODE), for rapid and generalizable dynamics learning.
• To enable modeling of unseen dynamical systems and inverse inference of physical parameters without prior knowledge.
• To embed physical knowledge as inductive biases within the neural network architecture.

Main Methods:

• A bilevel optimization framework is employed, with an outer level learning common force field forms and an inner level adapting to individual systems.
• The method learns 'metaknowledge' about functional variations in force fields across different system instances.
• Incorporation of a priori physical knowledge (e.g., conservative forces, Euclidean symmetry) as inductive biases in the neural network.

Main Results:

• iMODE successfully learns generalizable dynamics applicable to systems not encountered during training.
• The method can model unseen systems within seconds, demonstrating significant speed improvements.
• iMODE effectively performs inverse inference, revealing physical parameters from observed system trajectories.

Conclusions:

• iMODE provides a powerful and efficient approach for learning generalizable dynamics and inferring physical parameters from data.
• The method's flexibility allows application to diverse dynamical systems with arbitrary types or numbers of physical parameters.
• Validated on multiple systems including bistable, double pendulum, Van der Pol, Slinky, and reaction-diffusion systems.