Acoustic simulations often face significant uncertainties due to limited knowledge of acoustic boundary conditions. While measuring the boundary admittance is challenging in practical applications, numerical inverse methods can be used to characterize the boundary conditions based on sound pressure data. However, conventional inverse methods require a validated forward model and can become impractical for computationally expensive simulation models. Over the past years, machine learning approaches have emerged as promising methods for scientific computing and data-driven modeling. Physics-informed neural networks incorporate physical prior knowledge into a neural network by adding the residual of the underlying partial differential equation to the loss function. Training the neural network minimizes the loss function, allowing the network to learn a solution that not only fits the training data but also satisfies the corresponding boundary value problem. In this study, physics-informed neural networks are trained to learn the sound pressure solution within two numerical examples governed by the Helmholtz equation without explicitly specifying the boundary conditions at selected boundaries. After training, the neural network’s prediction of the boundary admittance is evaluated and compared to the ground truth, initially assigned in the finite element reference solution. Additionally, the proposed method is validated using experimental data obtained from an acoustic impedance tube measurement. The results show that physics-informed neural networks can accurately learn the sound pressure field and implicitly solve the inverse problem by providing an accurate estimate of the underlying boundary admittance, even in the case of spatially varying boundary conditions.

中文翻译：

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用于声学边界导纳估计的物理信息神经网络

由于对声学边界条件的了解有限，声学模拟常常面临很大的不确定性。虽然测量边界导纳在实际应用中具有挑战性，但可以使用数值反演方法来基于声压数据来表征边界条件。然而，传统的反演方法需要经过验证的正演模型，并且对于计算成本昂贵的仿真模型来说可能变得不切实际。在过去的几年里，机器学习方法已成为科学计算和数据驱动建模的有前途的方法。物理信息神经网络通过将基础偏微分方程的残差添加到损失函数中，将物理先验知识合并到神经网络中。训练神经网络最小化损失函数，让网络学习到一个既适合训练数据又满足相应边值问题的解决方案。在这项研究中，物理信息神经网络经过训练，可以学习由亥姆霍兹方程控制的两个数值示例内的声压解，而无需明确指定所选边界的边界条件。训练后，将评估神经网络对边界导纳的预测，并将其与最初在有限元参考解中分配的地面实况进行比较。此外，所提出的方法使用从声阻抗管测量获得的实验数据进行了验证。结果表明，即使在边界条件空间变化的情况下，基于物理的神经网络也可以通过提供对基础边界导纳的准确估计来准确学习声压场并隐式解决反演问题。