Emulation, Inverse Problem and Probabilistic Modeling of Physics-Based Systems

Owing to their strong expressive power and great flexibility, deep neural network-based surrogate models have tremendously advanced the development of digital twins across a wide spectrum of physics-based systems. Apart from traditional architectures, modern artificial intelligence techniques such as normalizing flows and variational auto-encoder further equip the data-driven modeling with probabilistic perspectives and generative capabilities. However, among diverse aspects of studying a physical system, emulating the forward problem has been a primary interest, while other crucial components, like inverse problem and parameter identifiability analysis receive relatively less attention. In this work, we propose InVAErt networks, a data-driven framework that comprehensively synthesizes physics-based systems, including input-to-output forward emulation, probabilistic modeling of outputs, solving inverse problem in an amortized fashion, as well as addressing input parameter non-identifiability. In particular, the augmentation of a latent space constructed through a variational network facilitates the discovery of the structurally non-identifiable manifold embedded in the input space that maps to a common output. In addition, several approaches of dealing with practical identifiability induced by missing observations in the outputs, measurement noise and mis-specification error are also proposed, including a physics-based missing data imputation method and artificial noise injection during network training. For validation, a series of numerical experiments are carried out, starting from simple maps, to nonlinear dynamical systems, space-time PDEs and large scale hemodynamic models used for real-time inference of physiological states from real electronic health records (EHR).