Physics-informed neural network and reduced order modeling in the context of variational multiscale method
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In this work the finite element framework for reduced order modeling (ROM) and physics-informed neural network (PINN) in the context of variational multiscale (VMS) methods is presented. The reduced order model in the current work is based on POD-Galerkin approach and fully-connected dense neural network architecture is chosen with hyperbolic tangent activation function for PINN. The developed framework is validated on several benchmark cases including vortex-shedding behind a 2D cylinder, turbulence generated on a 2D backward-facing step, 1D harmonic oscillator and Burgers' equation and 2D channel flow simulation with a focus on exploring diverse applications in aerospace and environmental flow problems.
