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

TL;DR

InVAErt networks provide a versatile data-driven framework for modeling, inverting, and analyzing physical systems, capturing complex behaviors and uncertainties through a combination of neural network components.

Contribution

This work introduces InVAErt networks, a novel framework combining deterministic and probabilistic models for system synthesis and identifiability analysis.

Findings

Effective modeling of linear and nonlinear maps

Successful application to dynamical systems and PDEs

Insights into loss function penalty coefficient selection

Abstract

Use of generative models and deep learning for physics-based systems is currently dominated by the task of emulation. However, the remarkable flexibility offered by data-driven architectures would suggest to extend this representation to other aspects of system synthesis including model inversion and identifiability. We introduce inVAErt (pronounced "invert") networks, a comprehensive framework for data-driven analysis and synthesis of parametric physical systems which uses a deterministic encoder and decoder to represent the forward and inverse solution maps, a normalizing flow to capture the probabilistic distribution of system outputs, and a variational encoder designed to learn a compact latent representation for the lack of bijectivity between inputs and outputs. We formally investigate the selection of penalty coefficients in the loss function and strategies for latent space sampling, since we find that these significantly affect both training and testing performance. We validate our framework through extensive numerical examples, including simple linear, nonlinear, and periodic maps, dynamical systems, and spatio-temporal PDEs.