FastVPINNs: Tensor-Driven Acceleration of VPINNs for Complex Geometries
This addresses a scalability bottleneck for researchers and engineers using physics-informed neural networks in scientific machine learning, though it is an incremental advancement.
The paper tackled the computational inefficiency of traditional hp-VPINNs for solving partial differential equations in complex geometries, achieving a 100-fold reduction in median training time per epoch with FastVPINNs while improving speed and accuracy.
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.