In this work, we train conditional Wasserstein generative adversarial networks to effectively sample from the posterior of physics-based Bayesian inference problems. The generator is constructed using a U-Net architecture, with the latent information injected using conditional instance normalization. The former facilitates a multiscale inverse map, while the latter enables the decoupling of the latent space dimension from the dimension of the measurement, and introduces stochasticity at all scales of the U-Net. We solve PDE-based inverse problems to demonstrate the performance of our approach in quantifying the uncertainty in the inferred field. Further, we show the generator can learn inverse maps which are local in nature, which in turn promotes generalizability when testing with out-of-distribution samples.
翻译:在这项工作中,我们培训了有条件的瓦森斯坦基因对抗网络,以便有效地从基于物理学的贝叶斯论推论问题的后台取样;发电机是使用U-Net结构建造的,其潜在信息是使用有条件实例的正常化注入的;前者促进多尺度反向图,而后者则使潜在空间层面与测量的层面脱钩,并在U-Net的所有尺度上引入随机性。我们解决基于PDE的反向问题,以表明我们在量化推断领域不确定性方面的做法的绩效。此外,我们展示出,发电机可以学习具有当地性质的反向地图,这反过来又有助于在用分布样本进行测试时的通用性。