Nonlinear Isometric Manifold Learning for Injective Normalizing Flows

arXiv (Cornell University)

Abstract

To model manifold data using normalizing flows, we employ isometric autoencoders to design embeddings with explicit inverses that do not distort the probability distribution. Using isometries separates manifold learning and density estimation and enables training of both parts to high accuracy. Thus, model selection and tuning are simplified compared to existing injective normalizing flows. Applied to data sets on (approximately) flat manifolds, the combined approach generates high-quality data.

Authors 4

1. Eike Cramer Aachen

   Forschungszentrum Jülich · RWTH Aachen University

   Affiliation as printed

   Forschungszentrum Jülich GmbH , Institute of Energy and Climate Research , Energy Systems Engineering (IEK- 10) , Jülich 52425 , Germany

   RWTH Aachen University , Process Systems Engineering (AVT.SVT) , Aachen 52074 , Germany

2. Alexander Mitsos
3. Raul F. Tempone Aachen Chair of Mathematics for Uncertainty Quantification

   King Abdullah University of Science and Technology · RWTH Aachen University

   Affiliation as printed

   King Abdullah University of Science and Technology (KAUST) , Computer, Electrical, and Mathematical Sciences & Engineering Division (CEMSE) , Saudi Arabia

   RWTH Aachen University , Chair of Mathematics for Uncertainty Quantification , Aachen 52062 , Germany

4. Manuel Dahmen

   Forschungszentrum Jülich

   Affiliation as printed

   Forschungszentrum Jülich GmbH , Institute of Energy and Climate Research , Energy Systems Engineering (IEK- 10) , Jülich 52425 , Germany