Title: InVAErt networks: a data-driven framework for model synthesis and identifiability analysis
Abstract: Applications of generative modeling and deep learning in physics-based systems have traditionally focused on building emulators, i.e. computational inexpensive approximations of the input-to-output map. However, the remarkable flexibility of data-driven architectures suggests broadening their scope to include aspects such as model inversion and identifiability. We introduce InVAErt networks, a framework for data-driven analysis and synthesis of parametric physical systems. An inVAErt network consists of an encoder-decoder pair representing the forward and inverse solution maps, a density estimator which captures the probabilistic distribution of the system outputs, and a variational encoder which learns a compact latent representation that restores bijectivity between inputs and outputs. We validated our approach through extensive numerical experiments, including simple linear, nonlinear, and periodic maps, dynamical systems, and spatio-temporal PDEs. I will also discuss an application in amortized physiologic inversion for a stiff lumped-parameter network circulatory model with 23 inputs and 15 outputs.
Speaker Bio: Daniele Schiavazzi is an associate professor in the Applied and Computational Mathematics and Statistics Department, and a concurrent associate professor in the Aerospace and Mechanical Engineering Department at the University of Notre Dame. His main research interests are in model-based inference and uncertainty quantification. He is particularly interested in developing computational tools and numerical methods for describing systems in physics or physiology governed by ordinary and partial differential equations, and efficiently solving direct and inverse problems using multi-fidelity approaches. He is also interested in using data-driven model synthesis to develop predictive digital twins, and in the analysis of parameter identifiability. He received an NSF CAREER award (2020-2025), a DARPA Young Faculty Award (2018), an American Heart Association Postdoctoral Fellowship (2015-2016), and was an Advisor to X (formerly Google X) in 2019.
