  The articulatory geometric configurations of the vocal tract and the acoustic
properties of the resultant speech sound are considered to have a strong causal
relationship. This paper aims at finding a joint latent representation between
the articulatory and acoustic domain for vowel sounds via invertible neural
network models, while simultaneously preserving the respective domain-specific
features. Our model utilizes a convolutional autoencoder architecture and
normalizing flow-based models to allow both forward and inverse mappings in a
semi-supervised manner, between the mid-sagittal vocal tract geometry of a two
degrees-of-freedom articulatory synthesizer with 1D acoustic wave model and the
Mel-spectrogram representation of the synthesized speech sounds. Our approach
achieves satisfactory performance in achieving both articulatory-to-acoustic as
well as acoustic-to-articulatory mapping, thereby demonstrating our success in
achieving a joint encoding of both the domains.
