  Multiphysics problems that are characterized by complex interactions among
fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are
inherently challenging due to their coupled nature. While experimental data on
certain state variables may be available, integrating these data with numerical
solvers remains a significant challenge. Physics-informed neural networks
(PINNs) have shown promising results in various engineering disciplines,
particularly in handling noisy data and solving inverse problems. However,
their effectiveness in forecasting nonlinear phenomena in multiphysics regimes
is yet to be fully established. This study introduces NeuroSEM, a hybrid
framework integrating PINNs with the high-fidelity Spectral Element Method
(SEM) solver, Nektar++. NeuroSEM leverages strengths of both PINNs and SEM,
providing robust solutions for multiphysics problems. PINNs are trained to
assimilate data and model physical phenomena in specific subdomains, which are
then integrated into Nektar++. We demonstrate the efficiency and accuracy of
NeuroSEM for thermal convection in cavity flow and flow past a cylinder. The
framework effectively handles data assimilation by addressing those subdomains
and state variables where data are available. We applied NeuroSEM to the
Rayleigh-B\'enard convection system, including cases with missing thermal
boundary conditions. Our results indicate that NeuroSEM accurately models the
physical phenomena and assimilates the data within the specified subdomains.
The framework's plug-and-play nature facilitates its extension to other
multiphysics or multiscale problems. Furthermore, NeuroSEM is optimized for an
efficient execution on emerging integrated GPU-CPU architectures. This hybrid
approach enhances the accuracy and efficiency of simulations, making it a
powerful tool for tackling complex engineering challenges in various scientific
domains.
