  Variational Physics-Informed Neural Networks (VPINNs) utilize a variational
loss function to solve partial differential equations, mirroring Finite Element
Analysis techniques. Traditional hp-VPINNs, while effective for high-frequency
problems, are computationally intensive and scale poorly with increasing
element counts, limiting their use in complex geometries. This work introduces
FastVPINNs, a tensor-based advancement that significantly reduces computational
overhead and improves scalability. Using optimized tensor operations,
FastVPINNs achieve a 100-fold reduction in the median training time per epoch
compared to traditional hp-VPINNs. With proper choice of hyperparameters,
FastVPINNs surpass conventional PINNs in both speed and accuracy, especially in
problems with high-frequency solutions. Demonstrated effectiveness in solving
inverse problems on complex domains underscores FastVPINNs' potential for
widespread application in scientific and engineering challenges, opening new
avenues for practical implementations in scientific machine learning.
