We investigate the use of learning approaches to handle Bayesian inverse problems in a computationally efficient way when the signals to be inverted present a moderately high number of dimensions and are in large number. We propose a tractable inverse regression approach which has the advantage to produce full probability distributions as approximations of the target posterior distributions. In addition to provide confidence indices on the predictions, these distributions allow a better exploration of inverse problems when multiple equivalent solutions exist. We then show how these distributions can be used for further refined predictions using importance sampling, while also providing a way to carry out uncertainty level estimation if necessary. The relevance of the proposed approach is illustrated both on simulated and real data in the context of a physical model inversion in planetary remote sensing. The approach shows interesting capabilities both in terms of computational efficiency and multimodal inference.

我们研究了使用学习方法以计算有效的方式处理贝叶斯逆问题，当要反转的信号呈现出中等数量的维度并且数量很大时。我们提出了一种易于处理的逆回归方法，该方法具有产生完整概率分布作为目标后验分布的近似值的优势。除了提供预测的置信度指数外，当存在多个等效解决方案时，这些分布允许更好地探索逆问题。然后，我们展示了如何使用这些分布来使用重要性采样进行进一步细化的预测，同时还提供了一种在必要时进行不确定性水平估计的方法。在行星遥感物理模型反演的背景下，在模拟数据和真实数据上都说明了所提出方法的相关性。该方法在计算效率和多模式推理方面都显示出有趣的能力。