We propose and show the efficacy of a new method to address generic inverse
problems. Inverse modeling is the task whereby one seeks to determine the
control parameters of a natural system that produce a given set of observed
measurements. Recent work has shown impressive results using deep learning, but
we note that there is a trade-off between model performance and computational
time. For some applications, the computational time at inference for the best
performing inverse modeling method may be overly prohibitive to its use. We
present a new method that leverages multiple manifolds as a mixture of backward
(e.g., inverse) models in a forward-backward model architecture. These multiple
backwards models all share a common forward model, and their training is
mitigated by generating training examples from the forward model. The proposed
method thus has two innovations: 1) the multiple Manifold Mixture Network (MMN)
architecture, and 2) the training procedure involving augmenting backward model
training data using the forward model. We demonstrate the advantages of our
method by comparing to several baselines on four benchmark inverse problems,
and we furthermore provide analysis to motivate its design.

本研究提出并证明了一种新的逆问题解决方法，使用深度学习代替传统解析解，使用多种流形反向建模相结合的正向反馈模型架构，借助前向模型生成训练数据，用于在计算时间和模型性能之间取得平衡，通过对四项基准逆问题的比较，并对其设计进行分析来展示其优势。