mlsanityData to 14 Oct 2026

Physics-informed KAN PointNet: Deep learning for simultaneous solutions to inverse problems in incompressible flow on numerous irregular geometries

arXiv 2504.06327 ↗First posted 8 Apr 2025cs.LG physics.flu-dyncited by 3

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Abstract (arXiv)

Kolmogorov-Arnold Networks (KANs) have gained attention as an alternative to traditional multilayer perceptrons (MLPs) for deep learning applications in computational physics, particularly for solving inverse problems with sparse data, as exemplified by the physics-informed Kolmogorov-Arnold network (PIKAN). However, the capability of KANs to simultaneously solve inverse problems over multiple irregular geometries within a single training run remains unexplored. To address this gap, we introduce the physics-informed Kolmogorov-Arnold PointNet (PI-KAN-PointNet), in which shared KANs are integrated into the PointNet architecture to capture the geometric features of computational domains. The loss function comprises the squared residuals of the governing equations, computed via automatic differentiation, along with sparse observations and partially known boundary conditions. We construct shared KANs using Jacobi polynomials and investigate their performance by considering Jacobi polynomials of different degrees and types in terms of both computational cost and prediction accuracy. As a benchmark test case, we consider natural convection in a square enclosure with a cylinder, where the cylinder's shape varies across a dataset of 135 geometries. PI-KAN-PointNet offers two main advantages. First, it overcomes the limitation of current PIKANs, which are restricted to solving only a single computational domain per training run, thereby reducing computational costs. Second, when comparing the performance of PI-KAN-PointNet with that of the physics-informed PointNet using MLPs, we observe that, with approximately the same number of trainable parameters and comparable computational cost in terms of the number of epochs, training time per epoch, and memory usage, PI-KAN-PointNet yields more accurate predictions, particularly for values on unknown boundary conditions involving nonsmooth geometries.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 71 of its 142 references that are in the map. First posted on arXiv 8 Apr 2025.

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71 of 142 references.

References · 71

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  2. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,248
  3. 2017PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Spacecited by 4,401
  4. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  5. 2022Solving Quantitative Reasoning Problems with Language Modelscited by 1,392
  6. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 734
  7. 2017Frustum PointNets for 3D Object Detection from RGB-D Datacited by 640
  8. 2023Mathematical Capabilities of ChatGPTcited by 268
  9. 2023MathPrompter: Mathematical Reasoning using Large Language Modelscited by 236
  10. 2023Spherical Fourier Neural Operators: Learning Stable Dynamics on the Spherecited by 233
  11. 2021Gradient-enhanced physics-informed neural networks for forward and inverse PDE problemscited by 222
  12. 2024U-KAN Makes Strong Backbone for Medical Image Segmentation and Generationcited by 179
38 more
  1. 2020PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domaincited by 174
  2. 2024Kolmogorov-Arnold Networks are Radial Basis Function Networkscited by 128
  3. 2024Wav-KAN: Wavelet Kolmogorov-Arnold Networkscited by 122
  4. 2024Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximationcited by 118
  5. 2024A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networkscited by 104
  6. 2024Kolmogorov-Arnold Networks (KANs) for Time Series Analysiscited by 98
  7. 2024DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problemscited by 84
  8. 2020Physics informed deep learning for computational elastodynamics without labeled datacited by 80
  9. 2024Convolutional Kolmogorov-Arnold Networkscited by 77
  10. 2022Physics-informed neural networks for inverse problems in supersonic flowscited by 76
  11. 2024KAN or MLP: A Fairer Comparisoncited by 73
  12. 2024TKAN: Temporal Kolmogorov-Arnold Networkscited by 71
  13. 2024Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretabilitycited by 70
  14. 2021Physics-informed neural networks for solving Reynolds-averaged Navierunicodex2013Stokes equationscited by 68
  15. 2024Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networkscited by 67
  16. 2024fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functionscited by 64
  17. 2024KAN-ODEs: Kolmogorov-Arnold Network Ordinary Differential Equations for Learning Dynamical Systems and Hidden Physicscited by 59
  18. 2022Bayesian Physics-Informed Neural Networks for real-world nonlinear dynamical systemscited by 54
  19. 2024GKAN: Graph Kolmogorov-Arnold Networkscited by 53
  20. 2024A Temporal Kolmogorov-Arnold Transformer for Time Series Forecastingcited by 52
  21. 2024KAGNNs: Kolmogorov-Arnold Networks meet Graph Learningcited by 49
  22. 2024Kolmogorov-Arnold Network for Satellite Image Classification in Remote Sensingcited by 47
  23. 2022Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarioscited by 46
  24. 2024BSRBF-KAN: A combination of B-splines and Radial Basis Functions in Kolmogorov-Arnold Networkscited by 46
  25. 2020A Point-Cloud Deep Learning Framework for Prediction of Fluid Flow Fields on Irregular Geometriescited by 44
  26. 2024Demonstrating the Efficacy of Kolmogorov-Arnold Networks in Vision Taskscited by 40
  27. 2024Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networkscited by 38
  28. 2024KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Searchcited by 37
  29. 2024Exploring the Potential of Polynomial Basis Functions in Kolmogorov-Arnold Networks: A Comparative Study of Different Groups of Polynomialscited by 35
  30. 2024Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problemscited by 35
  31. 2024Unveiling the Power of Wavelets: A Wavelet-based Kolmogorov-Arnold Network for Hyperspectral Image Classificationcited by 34
  32. 2024Suitability of KANs for Computer Vision: A preliminary investigationcited by 34
  33. 2022A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: comparison with finite element methodcited by 33
  34. 2024GraphKAN: Enhancing Feature Extraction with Graph Kolmogorov Arnold Networkscited by 32
  35. 2024Kolmogorov-Arnold Graph Neural Networkscited by 32
  36. 2022Discovering plasticity models without stress datacited by 28
  37. 2023ChatGPT for Programming Numerical Methodscited by 26
  38. 2024A Benchmarking Study of Kolmogorov-Arnold Networks on Tabular Datacited by 25

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 2; 2026: 1.

3 papers.

  1. 2025LNN-PINN: A Unified Physics-Only Training Framework with Liquid Residual Blockscited by 3
  2. 2026Flow Matching and Diffusion Models via PointNet for Generating Fluid Fields on Irregular Geometriescited by 2
  3. 2025xLSTM-PINN: Memory-Gated Spectral Remodeling for Physics-Informed Learningcited by 0