DDDAS for Systems Analytics in Applied Mechanics

This contribution is comprised of two parts. In the first part we provide an overview of the Dynamically Data-Driven Applications Systems (DDDAS) concept, with particular emphasis on the analytics of systems coming from the field of Applied Mechanics and focusing on the applications to aerospace structures. Aerospace composite materials and structures exhibit a strong multiscale behavior, which necessitates the development of a multiscale DDDAS framework wherein measurements and models interact at all the relevant spatial scales of the system of interest to maximize the resulting predictive power. We present a large-scale structural system example where the combination of dynamic data and advanced models are needed to be truly predictive. In the second part we examine the Neural Network (NN)-based data-driven approaches for systems analytics in applied mechanics, in particular, the Physics-Informed Neural Networks (PINNs) framework. The main idea of PINNs is to compensate for the lack of sufficient volume of measured data by forcing the system to obey the laws of physics expressed in the form of boundary-value problems (BVPs) based on partial differential equations (PDEs). A distinguishing feature of PINNs is that the discretization of a BVP does not make use of traditional methods, but rather NNs themselves. We focus on the ability of the approaches, incorporating NNs (as a tool) into DDDAS, to model large-deformation elastoplastic behavior of solids and structures so that they can be seamlessly integrated into structural systems analytics and beyond.