InVAErt networks: a data-driven framework for model synthesis and identifiability analysis
This framework addresses the need for comprehensive data-driven synthesis and analysis in physics-based modeling, offering a novel approach but appearing incremental in its integration of existing components.
The authors tackled the problem of extending data-driven generative models beyond emulation to include model inversion and identifiability analysis for parametric physical systems, introducing inVAErt networks and validating them with numerical examples across linear, nonlinear, periodic maps, dynamical systems, and spatio-temporal PDEs.
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.