InVAErt networks: a data-driven framework for model synthesis and identifiability analysis

In the simulation of physical systems, an increase in model complexity directly corresponds to an increase in the simulation time, posing substantial limitations to the use of such models for critical applications that depend on timesensitive decisions. Therefore, fast emulators learned by data-driven architectures and integrated in algorithms for the solution of forward and inverse problems are becoming increasingly successful. On one hand, several contributions in the literature have proposed architectures for physics-based emulators designed to limit the number of model evaluations during training. These include, for example, physics-informed neural networks (PINN) [1], deep operator networks (DeepONet) [2], and transformers-based architectures [3]. On the other hand, generative approaches have been the subject of significant recent research due to their flexibility to quantify uncertainty in the predicted outputs. Unlike traditional deep learning tasks, generative models focus on capturing a distributional characterization of the latent variables, providing an improved understanding, and a superior way to interact with a given system. Examples in this context include Gaussian Processes [4], Bayesian networks [5], generative adversarial networks (GAN) [6], diffusion models [7], optimal transport [8], normalizing flow [9, 10] and Variational Auto-Encoders (VAE) [11]. When using data-driven emulators in the context of inverse problems, other difficulties arise. Inverse problem are often ill-posed as a result of non-uniqueness of solutions, or of ill-conditioning due to high-dimensionality, data-sparsity, noise-corruption, and nonlinear response of the physical systems [12, 13, 14, 15, 16].