Physics-informed deep generative models
This work addresses uncertainty propagation in physical systems where data is scarce, offering a domain-specific solution for fields like engineering and physics.
The paper tackles the problem of propagating uncertainty through complex physical systems by introducing physics-informed constraints into deep generative models, resulting in a scalable framework for uncertainty characterization with demonstrated effectiveness in a transport dynamics example.
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.