A physical-generative framework for data-driven modeling with uncertainty quantification
Please login to view abstract download link
In the big data era, advancements in sensor technology have enabled frequent access to rich spatio-temporal datasets. This shift has introduced a new paradigm where predictive dynamical models can be derived automatically from data streams, significantly reducing the need for extensive prior knowledge and manual tuning. We propose a generative framework designed to extract physical models directly from raw data. Our method focuses on uncovering low-dimensional latent variables and building a dynamical model within this reduced space. This is achieved by integrating variational autoencoders for dimensionality reduction with Variational Identification of Nonlinear Dynamics (VINDy) to learn a probabilistic dynamical model from a set of candidate features. After training, the model is used in an online generative phase to compute full-time solutions for novel control inputs or initial conditions. The probabilistic nature of the framework also allows for uncertainty quantification, providing uncertainty-aware predictions. We validate the performance of our approach across a variety of high-dimensional, nonlinear dynamical systems.
