ncts

Digital twins (DTs) are digital replicas of systems and processes. At the core of a DT is a physical/mathematical model which captures the behavior of the real system across temporal and spatial scales. One of the key roles of DTs is enabling “what if” scenario testing of hypothetical simulations to understand the implications at any point throughout the life cycle of the process, to monitor the process, and to calibrate parameters to match the actual process. In this talk, we will present rigorous enabling methods using deep neural networks: 1) a unified and constructive universal framework to understand why many neural networks can approximate any functions in any desired accuracy; 2) mcTangent (a model-constrained tangent slope learning) approach for learning long-time solutions of dynamical systems; and 3) TNet (a model-constrained Tikhonov network) approach for learning inverse solutions. Both theoretical and numerical results for various problems, including transport, heat, Burgers, and Navier-Stokes equations, will be presented.