PG-KINN

PG-KINN: Petrov-Galerkin formulation for Kolmogorov-Arnold Networks applied to forward and inverse PDEs

Researchers propose PG-KINN, a physics-informed neural network that combines Kolmogorov-Arnold Networks (KANs) as the trial space with an independent piecewise-polynomial test space under a Petrov-Galerkin weak formulation. The approach uses integration by parts and Gauss-Legendre quadrature to reduce differentiation order and improve conditioning, enabling application to non-self-adjoint, nonlinear, and inverse problems where energy-form methods fail. On benchmarks including crack singularities, hyperelasticity, and inverse parameter identification, PG-KINN outperforms both MLP-based physics-informed networks and KAN-based strong/energy-form alternatives (PIKAN).