PINN + Poisson + Laplace¶

Notebook: PINN_Poisson_Laplace_Tutorial.ipynb

This tutorial introduces PINN1D and PINN2D on analytic Poisson problems. The networks are trained with physics-informed residuals, and uncertainty is quantified with last-layer Laplace over sparse supervised anchor data. The current notebook version uses richer interior anchors, an Adam -> LBFGS schedule, and compares diag with block_diag last-layer curvature before displaying the final uncertainty map.

Primary references:

• Raissi, Perdikaris, & Karniadakis (2019), Physics-informed neural networks
• MacKay (1992), A Practical Bayesian Framework for Backpropagation Networks
• Ritter et al. (2018), A Scalable Laplace Approximation for Neural Networks