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.

应用深度生成模型通过物理学定理来传递极高复杂物理系统中的不确定性。我们构建出一个隐式变分推断公式，并顺利地运用物理学原理作为模型输出的约束条件。这让模型在面对高成本数据采集以及通常小型训练数据集的物理系统建模时具备了一种可扩展的方法来描述随机输入或观测和物理系统输出的不确定性，并以传输动态为规范示例来验证了方法的有效性。

基于物理先验的深度生成模型