Variational Integrator Networks for Physically Structured Embeddings
This work addresses the need for physically structured embeddings in dynamical systems modeling, offering a novel approach that is incremental in combining neural networks with geometric principles.
The authors tackled the problem of learning representations of dynamical systems by proposing variational integrator networks, which preserve geometric structure and enable accurate long-term prediction, interpretability, and data-efficient learning, demonstrating accurate learning from noisy phase space observations and image pixels.
Learning workable representations of dynamical systems is becoming an increasingly important problem in a number of application areas. By leveraging recent work connecting deep neural networks to systems of differential equations, we propose \emph{variational integrator networks}, a class of neural network architectures designed to preserve the geometric structure of physical systems. This class of network architectures facilitates accurate long-term prediction, interpretability, and data-efficient learning, while still remaining highly flexible and capable of modeling complex behavior. We demonstrate that they can accurately learn dynamical systems from both noisy observations in phase space and from image pixels within which the unknown dynamics are embedded.