�Generative Modeling of Regular and Irregular Time Series Data
via Koopman Variational Autoencoders (VAEs)�
1
Scientific Achievement
We present Koopman VAE, a new generative framework with a novel model prior suitable for regular and irregular sampled data. It utilizes a linear map inspired by Koopman theory to represent latent conditional prior dynamics. This allows for the integration of domain knowledge through spectral tools.
Significance and Impact
Scientists encounter challenges due to the inherent sparsity of observational weather data, particularly in specific geographical regions. We demonstrate on a challenging climate dataset that our model approximates well the associated density distribution, and it generates accurate temperature long-term signals from sparse measurement data. Moreover, we show state-of-the-art results in regular and irregular settings on several synthetic and real-world datasets.
Remarkably, we show that our Koopman VAE (A) is able to generate a four-month long signal (B) that resembles the ground truth for unseen geospatial coordinates. Our results emphasize the ability of our model to generate real-world scientific data.
Technical Approach
We augment a VAE model with a Koopman operator module.
Our approach builds on the assumption that there exists a learnable nonlinear function, which is mapping inputs to a linear latent space.
This enables us to solve a linear system to get a Koopman Operator.
We introduce an additional predictive loss term that promotes linearity.
PI(s)/Facility Lead(s): Lenny Oliker (LBL)
Collaborating Institutions: ICSI, UC Berkeley, Ben Gurion University of the Negev