Accelerated Training of Physics-Informed Neural Networks (PINNs) using Meshless Discretizations
Auteurs : Ramansh Sharma, Varun Shankar
Résumé : We present a new technique for the accelerated training of physics-informed neural networks (PINNs): discretely-trained PINNs (DT-PINNs). The repeated computation of partial derivative terms in the PINN loss functions via automatic differentiation during training is known to be computationally expensive, especially for higher-order derivatives. DT-PINNs are trained by replacing these exact spatial derivatives with high-order accurate numerical discretizations computed using meshless radial basis function-finite differences (RBF-FD) and applied via sparse-matrix vector multiplication. The use of RBF-FD allows for DT-PINNs to be trained even on point cloud samples placed on irregular domain geometries. Additionally, though traditional PINNs (vanilla-PINNs) are typically stored and trained in 32-bit floating-point (fp32) on the GPU, we show that for DT-PINNs, using fp64 on the GPU leads to significantly faster training times than fp32 vanilla-PINNs with comparable accuracy. We demonstrate the efficiency and accuracy of DT-PINNs via a series of experiments. First, we explore the effect of network depth on both numerical and automatic differentiation of a neural network with random weights and show that RBF-FD approximations of third-order accuracy and above are more efficient while being sufficiently accurate. We then compare the DT-PINNs to vanilla-PINNs on both linear and nonlinear Poisson equations and show that DT-PINNs achieve similar losses with 2-4x faster training times on a consumer GPU. Finally, we also demonstrate that similar results can be obtained for the PINN solution to the heat equation (a space-time problem) by discretizing the spatial derivatives using RBF-FD and using automatic differentiation for the temporal derivative. Our results show that fp64 DT-PINNs offer a superior cost-accuracy profile to fp32 vanilla-PINNs.
Explorez l'arbre d'article
Cliquez sur les nœuds de l'arborescence pour être redirigé vers un article donné et accéder à leurs résumés et assistant virtuel
Recherchez des articles similaires (en version bêta)
En cliquant sur le bouton ci-dessus, notre algorithme analysera tous les articles de notre base de données pour trouver le plus proche en fonction du contenu des articles complets et pas seulement des métadonnées. Veuillez noter que cela ne fonctionne que pour les articles pour lesquels nous avons généré des résumés et que vous pouvez le réexécuter de temps en temps pour obtenir un résultat plus précis pendant que notre base de données s'agrandit.