Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

Area of Science:

• Computational Science
• Machine Learning
• Physics

Background:

• Predicting spatio-temporal dynamics is crucial but computationally intensive with traditional methods.
• Data-driven deep learning offers an alternative for modeling complex system evolution.

Purpose of the Study:

• Introduce the Latent Dynamics Network (LDN) architecture.
• Enable accurate prediction of system evolution in low-dimensional spaces for potentially non-Markovian systems.

Main Methods:

• Developed a novel deep learning architecture, the Latent Dynamics Network (LDN).
• LDNs automatically discover low-dimensional manifolds and learn system dynamics concurrently.
• The method avoids auto-encoder training and high-dimensional space operations.

Main Results:

• LDNs achieve superior accuracy, with normalized errors 5 times smaller than state-of-the-art methods.
• Significantly fewer trainable parameters (over 10 times fewer) are required.
• The approach excels in highly nonlinear problems and enables time-extrapolation predictions without fixed grids.

Conclusions:

• Latent Dynamics Networks offer a lightweight, efficient, and accurate solution for modeling spatio-temporal dynamics.
• This architecture advances data-driven approaches for scientific prediction and simulation.