A NURBS-based parameterization physics-informed neural network with an adaptive architecture for solving PDEs

Physical Information Neural Network (PINN) has become essential tools in scientific computing, yet their performance is often constrained in engineering applications involving irregular physical domains. To address this challenge, we precisely model irregular physical domains using non-uniform rational B-spline maps and integrate them with PINN. But this will bring a unique training ill-posed problem, then we developed NSGH-PINN by constructing a sine-enhanced adaptive activation function and coordinating the adaptive loss function with a gradient-based loss weighting strategy. Analysis from various numerical experiments demonstrates that NSGH-PINN reduces the L 2 error by one to two orders of magnitude compared to baseline. It also consistently outperforms other advanced variants adapted to the same geometric framework. The proposed framework enables the broader application of PINN in scientific and engineering simulations.