PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs

Amirhossein Sadr, Nima Soltani, Vahideh Moghtadaiee, Aida Pakniyat, Dara Rahmati et al.|July 22, 2026arXiv

Key Takeaway

By pairing KANs with Petrov-Galerkin weak formulations instead of strong-form residuals, you get better numerical stability, lower computational cost, and broader applicability to real physics problems—without sacrificing accuracy.

Summary

This paper introduces PG-KINN, a physics-informed neural network that combines Kolmogorov-Arnold Networks (KANs) with a Petrov-Galerkin mathematical formulation to solve differential equations.

architecture reasoning

Key Terms

physics-informed-neural-network kolmogorov-arnold-network petrov-galerkin-method weak-form-residual