PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs
Physics-informed learning of partial differential equations (PDEs) has been dominated by multilayer perceptrons (MLPs), whose spectral bias and dense parameterization limit both accuracy and interpretability. Kolmogorov Arnold Networks (KANs) mitigate these limitations because their learnable spline activations are structurally aligned with the piecewise-polynomial bases of classical discretizations. However, the way a PDE is cast into a loss functional is as decisive as the choice of approximator: strong-form residual minimization requires high-order derivatives and heavily weighted losses, t
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- PossiblePossibly related (embedding) · 58%Principled approaches for extending neural architectures to function spaces for operator learning →
- PossiblePossibly related (embedding) · 49%Hamiltonian Neural Networks from a Differential Geometry Perspective [D] →
- LinkedLinked via arxiv author · 85%Amirhossein Sadr →
“PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs”
- LinkedLinked via arxiv author · 85%Nima Soltani →
“PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs”
- LinkedLinked via arxiv author · 85%Vahideh Moghtadaiee →
“PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs”
- LinkedLinked via arxiv author · 85%Aida Pakniyat →
“PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs”
- LinkedLinked via arxiv author · 85%Dara Rahmati →
“PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs”
- LinkedLinked via arxiv author · 85%Saeid Gorgin →
“PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs”