Prof. Sashikumaar Ganesan, Thivin Anandh and Divij Ghose presented their work on FastVPINNs at CRUNCH Lab Seminar held by Prof. George Karniadakis group on June 21-2024.
Abstract for the Talk:
Variational Physics-Informed Neural Networks (VPINNs) solve partial differential equations (PDEs) using a variational loss function, similar to Finite Element Methods. While hp-VPINNs are generally more effective than PINNs, they are computationally intensive and do not scale well with increasing element counts. This work introduces FastVPINNs, a tensor-based framework that significantly reduces training time and handles complex geometries. Optimized tensor operations in FastVPINNs achieve up to a 100-fold reduction in median training time per epoch compared to traditional hp-VPINNs. With the right hyperparameters, FastVPINNs can outperform conventional PINNs in both speed and accuracy, particularly for problems with high-frequency solutions.
The proposed method will be demonstrated with scalar and vector problems, showcasing its versatility and effectiveness in various applications.
Youtube Link: https://www.youtube.com/watch?v=YAxf4gOdehQ