Physics-informed deep generative models

TL;DR

This paper introduces a physics-informed deep generative modeling framework that incorporates physical laws via PDE constraints, enabling effective uncertainty quantification in complex physical systems with limited data.

Contribution

It proposes an implicit variational inference approach that enforces physical laws as constraints, improving training of probabilistic models for physical systems with scarce data.

Findings

Effective uncertainty propagation in transport dynamics

Regularization via physics-informed constraints improves model training

Scalable framework for physical systems with limited data

Abstract

We consider the application of deep generative models in propagating uncertainty through complex physical systems. Specifically, we put forth an implicit variational inference formulation that constrains the generative model output to satisfy given physical laws expressed by partial differential equations. Such physics-informed constraints provide a regularization mechanism for effectively training deep probabilistic models for modeling physical systems in which the cost of data acquisition is high and training data-sets are typically small. This provides a scalable framework for characterizing uncertainty in the outputs of physical systems due to randomness in their inputs or noise in their observations. We demonstrate the effectiveness of our approach through a canonical example in transport dynamics.