An interactive demo for our paper. Pick a benchmark problem, a model type, and an FDM grid size below — then hit Run Experiment to see how well our error estimation tracks the true PINN error, and how it compares to the FDM baseline.
No model selected
nx × nt (or nx × ny) for FDM solver
Heatmaps
PINN Prediction
True Solution
Estimated Error |eres| (our method)
Slice Plot — —
PINN vs Exact Solution
Error Comparison
t =—
Why is the error zero at the edges? The PINN is hard-constrained —
initial and boundary conditions are built directly into the network's output, so they are
satisfied exactly by construction. As a result, the error is always exactly zero at the
domain boundaries (and at t = 0 for time-dependent problems), which you'll
notice when moving the slider to the edges.