This work describes a novel data-driven latent space inference framework built on paired autoencoders to handle observational inconsistencies when solving inverse problems. Our approach uses two autoencoders, one for the parameter space and one for the observation space, connected by learned mappings between the autoencoders' latent spaces. These mappings enable a surrogate for regularized inversion and optimization in low-dimensional, informative latent spaces. Our flexible framework can work with partial, noisy, or out-of-distribution data, all while maintaining consistency with the underlying physical models. The paired autoencoders enable reconstruction of corrupted data, and then use the reconstructed data for parameter estimation, which produces more accurate reconstructions compared to paired autoencoders alone and end-to-end encoder-decoders of the same architecture, especially in scenarios with data inconsistencies. We demonstrate our approaches on two imaging examples in medical tomography and geophysical seismic-waveform inversion, but the described approaches are broadly applicable to a variety of inverse problems in scientific and engineering applications.

翻译：本研究提出了一种新颖的数据驱动隐空间推断框架，该框架建立在配对自编码器基础上，用于解决反问题时处理观测数据的不一致性。我们的方法使用两个自编码器，一个用于参数空间，另一个用于观测空间，并通过学习到的两个自编码器隐空间之间的映射进行连接。这些映射使得在低维且信息丰富的隐空间中进行正则化反演和优化的替代成为可能。我们的灵活框架能够处理部分、含噪或分布外数据，同时保持与底层物理模型的一致性。配对自编码器能够重建损坏的数据，然后利用重建后的数据进行参数估计，与单独的配对自编码器以及相同架构的端到端编码器-解码器相比，该方法能够产生更精确的重建结果，尤其是在数据不一致的场景下。我们在医学层析成像和地球物理地震波形反演两个成像示例上验证了所提出的方法，但所述方法广泛适用于科学和工程应用中的各类反问题。