2018/12/09 by Yibo Yang, Paris Perdikaris, Yang, Yibo +1 · 3 citations
Computer Science · Physics and Astronomy · #Computational Physics and Python Applications #FOS: Computer and information sciences #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.1812.03511
openalex publication_date 2018/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.