A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks

Computer Methods in Applied Mechanics and Engineering, Год журнала: 2024, Номер 431, С. 117290 - 117290

Опубликована: Авг. 19, 2024

Язык: Английский

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Kolmogorov–Arnold PointNet: Deep learning for prediction of fluid fields on irregular geometries

Computer Methods in Applied Mechanics and Engineering, Год журнала: 2025, Номер 439, С. 117888 - 117888

Опубликована: Март 11, 2025

Язык: Английский

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Three operator learning models for solving boundary integral equations in 2D connected domains

Applied Mathematical Modelling, Год журнала: 2025, Номер unknown, С. 116034 - 116034

Опубликована: Фев. 1, 2025

Язык: Английский

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Energy-Dissipative Evolutionary Kolmogorov–Arnold Networks for Complex Pde Systems

Опубликована: Янв. 1, 2025

Язык: Английский

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The Application of the Novel Kolmogorov–Arnold Networks for Predicting the Fundamental Period of RC Infilled Frame Structures

International journal of mechanical system dynamics, Год журнала: 2025, Номер unknown

Опубликована: Март 18, 2025

ABSTRACT The fundamental period is a crucial parameter in structural dynamics that informs the design, assessment, and monitoring of structures to ensure safety stability buildings during earthquakes. Numerous machine‐learning deep‐learning approaches have been proposed predict infill‐reinforced concrete frame structures. However, challenges remain, including insufficient prediction accuracy excessive computational resource demands. This study aims provide new paradigm for accurately efficiently predicting periods, namely, Kolmogorov–Arnold networks (KANs) their variants, especially radial basis function KANs (RBF‐KANs). are formulated based on representation theorem, positioning them as promising alternative multilayer perceptron. In this research, we compare performance against fully connected neural (FCNNs) context prediction. mutual information method was employed analysis dependencies between features FP4026 data set. Nine predictive models, KANs, F‐KANs, FCNN‐2, FCNN‐11, CatBoost, Support Vector Machine, others, were constructed compared, with hyperparameters determined by Optuna, which will highlight optimal model amongst F‐KANs models. Numerical results manifest highest yielded R 2 = 0.9948, offers an explicit form formula. Lastly, further dive into explainability interpretability revealing number stories opening percentage significant effect results.

Язык: Английский

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Physics-Informed Kolmogorov-Arnold Networks (PIKANs) for Solving the Buckley-Leverett Equation in Waterflooding Reservoirs

SPE Reservoir Simulation Conference, Год журнала: 2025, Номер unknown

Опубликована: Март 18, 2025

Abstract Kolmogorov-Arnold Networks (KANs), introduced in May 2024, present a novel network structure. Early researches show they outperform Multi-Layer Perceptrons (MLPs) computational efficiency, interpretability, and interaction. This paper aims to create the first physics-informed KAN (PIKAN) by replacing MLP with PINN, assessing its performance of solving fractional flow equation waterflooding reservoirs. To build PIKAN, spatial coordinates time serve as inputs, water saturation outputs. The loss function is derived from governing equation, initial, boundary conditions. It's optimized using Adam L-BFGS algorithms, updating PIKAN parameters. structure allows for automatic differentiation training, evaluation PIKANs conclude upon meeting accuracy criteria or reaching maximum optimization steps. We evaluate comparing their results high-fidelity benchmarks. findings reveal that can achieve similar prediction distribution MLP-based will experience more significant oscillations during training process compared PINN. In future, further improvement PIKAN's may be achieved improving optimizer study introduces promising into reservoir numerical simulations time, achieving pressure modeling heterogeneous reservoirs PIKAN. Compared existing developed demonstrates superior accuracy, robustness. provide initial reference developing universal rapid simulation history matching tools based on

Язык: Английский

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Extraction and reconstruction of variable-coefficient governing equations using Res-KAN integrating sparse regression

Physica D Nonlinear Phenomena, Год журнала: 2025, Номер unknown, С. 134689 - 134689

Опубликована: Май 1, 2025

Язык: Английский

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Intelligent monitoring of impact damage within concrete through deep learning-empowered electromechanical impedance technique

Measurement, Год журнала: 2025, Номер unknown, С. 117642 - 117642

Опубликована: Май 1, 2025

Язык: Английский

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Adaptive Method for Selecting Basis Functions in Kolmogorov–Arnold Networks for Magnetic Resonance Image Enhancement

Programming and Computer Software, Год журнала: 2025, Номер 51(3), С. 167 - 172

Опубликована: Май 11, 2025

Язык: Английский

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PDS-UKAN: Subdivision hopping connected to the U-KAN network for medical image segmentation

Computerized Medical Imaging and Graphics, Год журнала: 2025, Номер 124, С. 102568 - 102568

Опубликована: Май 23, 2025

Язык: Английский

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