<p>Physics-informed neural networks (PINNs) have proven to be a powerful tool for scattering simulation, leveraging physics principles to inform the learning process. When solving the acoustic scattering problem induced by the scatterer, conventional PINNs that rely on multilayer perceptrons (MLP) neglect the inherent acoustic field dependencies, thus failing to propagate globally the scattering characteristics and accurately capture nonlinear features near the scatterer boundary. Researchers often define explicit architectures or increase training parameter counts to capture these dependencies, yet this inevitably introduces either structural constraints or heightened computational costs. In this paper, we propose a novel framework based on the Kolmogorov–Arnold Network (KAN), termed PIKAN, to address this limitation. Leveraging KAN-driven plane wave expansion and the Sine activation function’s efficient plane wave learning capacity, PIKAN effectively captures both global dependencies and fine-grained scattering features in the scattered acoustic field. We evaluate the effectiveness and generalization performance of the PIKAN model across three typical scattering scenarios: high-frequency case, irregular scatterer, and multiple scattering, to validate its practicality. Experiments demonstrate that PIKAN achieves a superior balance between both accuracy and computational efficiency, when compared against state-of-the-art baselines and alternative activation functions. Moreover, integrating with the RAD method enhances the model’s flexibility and further improves its performance.</p>

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Physics-informed Kolmogorov-Arnold networks with residual-based adaptive distribution for scattered acoustic field prediction

  • Yi Ren,
  • Ligang Wang,
  • Haitao Ma

摘要

Physics-informed neural networks (PINNs) have proven to be a powerful tool for scattering simulation, leveraging physics principles to inform the learning process. When solving the acoustic scattering problem induced by the scatterer, conventional PINNs that rely on multilayer perceptrons (MLP) neglect the inherent acoustic field dependencies, thus failing to propagate globally the scattering characteristics and accurately capture nonlinear features near the scatterer boundary. Researchers often define explicit architectures or increase training parameter counts to capture these dependencies, yet this inevitably introduces either structural constraints or heightened computational costs. In this paper, we propose a novel framework based on the Kolmogorov–Arnold Network (KAN), termed PIKAN, to address this limitation. Leveraging KAN-driven plane wave expansion and the Sine activation function’s efficient plane wave learning capacity, PIKAN effectively captures both global dependencies and fine-grained scattering features in the scattered acoustic field. We evaluate the effectiveness and generalization performance of the PIKAN model across three typical scattering scenarios: high-frequency case, irregular scatterer, and multiple scattering, to validate its practicality. Experiments demonstrate that PIKAN achieves a superior balance between both accuracy and computational efficiency, when compared against state-of-the-art baselines and alternative activation functions. Moreover, integrating with the RAD method enhances the model’s flexibility and further improves its performance.