Development of Weak-Form Physics-Infused Reduced-Order Modeling With Applications

A novel physics-infused reduced-order modeling (PIROM) methodology has recently been developed for the synthesis of highly efficient, accurate, and generalizable non-linear reducedorder models. The PIROM consists of an augmented system of physics-based analytical equations that represents the domain physical knowledge, with a data-driven functional component that represents the unknown physical knowledge; the data-driven component may be in differential or algebraic form. For time-continuous systems, the unknown parameters for a data-driven component in differential form are often determined using standard adjoint-based optimization techniques that, however, may become numerically ill-conditioned as the training progresses. This motivates the development of the weak-form PIROM (PIROM-w), which circumvents the possibly ill-conditioned adjoint-based model training through a new weak-form optimization approach. The PIROM-w transforms the dynamical constraints associated with the augmented system into a set of integral constraints that are solved using standard methods of weighted residuals (MWR). The transformation of the constraints into integral form smooths the Lagrangian-based optimization search space by making the adjoint variables time-independent and transforming the differential adjoint problem into an algebraic one. In this work, PIROM-w is coupled with the ADAM algorithm for learning unknown dynamics in a forced pendulum system and a hypersonic panel flutter problem.