Generalizing to New Dynamical Systems via Frequency Domain Adaptation.

Area of Science:

• Physics
• Machine Learning
• Dynamical Systems

Background:

• Deep neural networks show promise in modeling complex physical dynamics.
• Current models struggle to generalize to new systems with varying environmental characteristics.

Purpose of the Study:

• To develop a parameter-efficient method for deep learning models to generalize across different physical dynamics and environments.
• To improve the adaptability of neural networks for modeling unseen systems.

Main Methods:

• Introduced Fourier Neural Simulator for Dynamical Adaptation (FNSDA).
• FNSDA utilizes adaptation in Fourier space to identify shareable dynamics and adjust environment-specific modes.
• Employs low-dimensional latent parameters for efficient generalization.

Main Results:

• FNSDA demonstrates superior or competitive generalization performance across four dynamic systems.
• Achieved significant reduction in parameter cost compared to existing methods.
• Effectively adapts to new dynamics by partitioning and adjusting Fourier modes.

Conclusions:

• FNSDA offers a parameter-efficient and adaptable solution for modeling complex physical dynamics.
• The method shows strong potential for generalizing deep learning models to unseen systems.
• Fourier space adaptation provides a robust mechanism for enhanced model generalization.