Automatic Differentiation from Scratch: How PyTorch Computes Gradients in Physics-Informed Neural Networks
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 $\nabla_θL$ of a loss that itself depends on $\hat{y}'(t)$. Using a 1-3-3-1 multilayer perceptron and the initial value problem $y'(t)+y(t)=0$, $y(0)=1$, we trace the complete pipeline at every node: the computational graph built during the forward pass, the reverse-mode backward traversal that computes all 22 parameter gradients in a single pass, a...
| Authors | Abdeladhim Tahimi |
|---|---|
| Primary category | cs.LG |
| Published | 13 June 2026 |
| Last updated at source | 13 June 2026 |
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