IGA-KAN: Isogeometric Analysis with Physics-Informed Closed-Form Kolmogorov-Arnold Networks for Forward and Inverse PDEs
math.NA, cs.LG, cs.NA
Submitted: 2026-10-05
Updated: 2026-10-05
Code: https://github.com/SimaNaraghi/iga-kan
Sources
- Characterizing possible failure modes in physics-informed neural networks
- KAN: Kolmogorov-Arnold Networks
- rKAN: Rational Kolmogorov-Arnold Networks
- Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networks
- PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs
- Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers
- A hybrid finite element/neural network solver and its application to the Poisson problem
- Super-Resolution of Elliptic PDE Solutions Using Least Squares Support Vector Regression
- Physics Informed Extreme Learning Machine (PIELM) -- A rapid method for the numerical solution of partial differential equations
- Local Extreme Learning Machines and Domain Decomposition for Solving Linear and Nonlinear Partial Differential Equations
- Bridging Traditional and Machine Learning-based Algorithms for Solving PDEs: The Random Feature Method
- Kolmogorov-Arnold PointNet: Deep learning for prediction of fluid fields on irregular geometries
- Weak-Form Evolutionary Kolmogorov-Arnold Networks for Solving Partial Differential Equations
- Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems
- Enriching continuous Lagrange finite element approximation spaces using neural networks
- Highly efficient NURBS-based isogeometric analysis for coupled nonlinear diffusion-reaction equations with and without advection
- Space-Time Isogeometric Analysis of Parabolic Evolution Equations
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