arXiv:2608. 11020v1 Announce Type: new Abstract: We systematically investigate finite-difference (FD) derivative computation in Physics-Informed Neural Networks (PINNs) as an alternative to automatic differentiation (AD).
By Maciej J. Mikulski, Tadeusz Uhl
arXiv:2607. 13042v1 Announce Type: new Abstract: This paper traces, with explicit numerical values, how PyTorch's automatic differentiation (AD) engine computes gradients for Physics-Informed Neural Network (PINN) training -- a setting that requires two levels of differentiation: computing the physics derivative $\hat{y}'(t)=d\hat{y}/dt$ through the network, and computing parameter gradients $\nabla_\theta L$ of a loss that itself depends on $\hat{y}'(t)$.
By Abdeladhim Tahimi
arXiv:2609.33078v2 Announce Type: replace
Abstract: Automatic differentiation (AD) lets neural networks compute derivatives of governing equations to machine precision, and this precision has made it...
By Ameya D. Jagtap
arXiv:2609.13171v1 Announce Type: new
Abstract: Physics-informed neural networks (PINNs) use automatic differentiation to impose differential-equation residuals, but good agreement in function values...
By Koji Koyamada
arXiv:2607. 18020v2 Announce Type: replace Abstract: Physics-Informed Neural Networks (PINNs) solve PDEs by incorporating physical constraints into neural-network training, but large-scale problems are limited by automatic-differentiation memory overhead and inefficient execution of grid-based PDE operators.
By Peiyu Zang, Bosen Xie, Ruoxiang Xu, Yongqiang Cai
arXiv:2607. 18020v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) solve PDEs by incorporating physical constraints into neural-network training, but large-scale problems are limited by automatic-differentiation memory overhead and inefficient execution of grid-based PDE operators.
By Peiyu Zang, Bosen Xie, Ruoxiang Xu, Yongqiang Cai