You only have a handful of noisy sensor readings of a field u(x) on [0, 1], but you know the governing Poisson equation -u''(x) = f(x) with homogeneous Dirichlet boundaries. A pure data fit will interpolate the sensors. A physics-informed network should reconstruct the field everywhere, including where you never measured.
Summarize the observation set before choosing a solver.
Implement explore_pinn(train_df) returning:
Evaluated server-side against a hidden test set.