Generation of realistic synthetic data using Multimodal Neural Ordinary Differential Equations

Conceptual introduction of the MultiNODEs

MultiNODEs represent an extension of the original NODEs framework¹⁴ that overcomes the limitations of its predecessor such that an application to incomplete datasets consisting of both static and time-dependent variables becomes feasible. Conceptually, MultiNODEs build on three key components (Fig. 1): (1) latent NODEs, (2) a variational autoencoder (more specifically a Heterogenous Incomplete Variational Autoencoder [HI-VAE], designed to handle multimodal data with missing values¹⁷), and (3) an implicit imputation layer¹⁸. The latent NODEs enable the learning and subsequent generation of continuous longitudinal variable trajectories. The longitudinal properties of the initial condition (i.e., the starting point for the ODE system solver of the latent NODEs) are defined by the output of a recurrent variational encoder that embeds the…