We propose a novel approach for solving inverse-problems with high-dimensional inputs and an expensive forward mapping. It leverages joint deep generative modelling to transfer the original problem spaces to a lower dimensional latent space. By jointly modelling input and output variables and endowing the latent with a prior distribution, the fitted probabilistic model indirectly gives access to the approximate conditional distributions of interest. Since model error and observational noise with unknown distributions are common in practice, we resort to likelihood-free inference with Approximate Bayesian Computation (ABC). Our method calls on ABC by Subset Simulation to explore the regions of the latent space with dissimilarities between generated and observed outputs below prescribed thresholds. We diagnose the diversity of approximate posterior solutions by monitoring the probability content of these regions as a function of the threshold. We further analyze the curvature of the resulting diagnostic curve to propose an adequate ABC threshold. When applied to a cross-borehole tomography example from geophysics, our approach delivers promising performance without using prior knowledge of the forward nor of the noise distribution.
翻译:我们提出了一个解决高维投入和昂贵前方绘图的反问题的新办法。它利用联合深基因模型将原始问题空间转移到低维潜层空间。通过联合建模输入和输出变量,并用先前的分布将潜在潜力缩小,安装的概率模型间接提供了大致的有条件利益分布条件。由于模型错误和观测噪音的分布不明,在实践中很常见,我们采用与Apbsbear Bayesian Computation(ABC)的无可能性推断。我们的方法通过子集模拟来探索潜伏空间的区域,这些区域在生成和观察到的输出低于规定阈值的产出之间存在差异。我们通过监测这些区域的概率内容作为临界值的函数,分析这些区域的近似后方解决方案的多样性。我们进一步分析由此得出的诊断曲线的曲线的曲解,以提出适当的ABC临界值。当我们应用地球物理的跨孔成像时,我们的方法在没有事先了解前方或噪音分布的情况下,能够带来良好的业绩。