3 papers
cs.LG2026
Automatic Differentiation from Scratch: How PyTorch Computes Gradients in Physics-Informed Neural Networks
Abdeladhim Tahimi
This paper traces, with explicit numerical values, how PyTorch's automatic differentiation (AD) engine computes gradients for Physics-Informed Neural Network (PINN) training -- a s…
math.OC2026
Dual-Network PINNs for Optimal Control: A Reproducible Benchmark on the Mass-Spring-Damper System
Abdeladhim Tahimi, Rinaldo Vieira da Silva Junior
This work presents a transparent and reproducible benchmark study of a direct dual-network Physics-Informed Neural Network (PINN) formulation for the optimal control of a mass-spri…
math.NA2026
Physics-Informed Neural Networks: A Didactic Derivation of the Complete Training Cycle
Abdeladhim Tahimi
This paper is a step-by-step, self-contained guide to the complete training cycle of a Physics-Informed Neural Network (PINN) -- a topic that existing tutorials and guides typicall…