Mixture Manifold Networks: A Computationally Efficient Baseline for Inverse Modeling

TL;DR

This paper introduces a computationally efficient inverse modeling method using a mixture of manifold models sharing a common forward model, improving training efficiency and performance on benchmark problems.

Contribution

The paper presents a novel Manifold Mixture Network architecture and a training procedure that augments backward model data using the forward model, offering a new efficient baseline for inverse problems.

Findings

Outperforms several baselines on four benchmark inverse problems.

Reduces training time compared to existing deep learning methods.

Provides analysis supporting the design choices.

Abstract

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.