Physics-informed networks get a coordinate change: CTPINN flattens steep gradients and recovers accuracy on boundary layers
Physics-informed neural networks (PINNs) often lose accuracy on PDEs with sharp gradients, partly because the network struggles to represent high-frequency variation. CTPINN adds a learnable coordinate transformation alongside the solution network, mapping the physical domain to a computational domain where the solution is approximately affine and gradients are more evenly distributed. The explicit construction restores accuracy on boundary-layer problems, and the implicit construction, plugged into PirateNet, SPINN and QRPINN, improves accuracy across several benchmark equations.