Physics-Informed Convolutional Neural Network with Bicubic Spline Interpolation for Sound Field Estimation
Physics-Informed Convolutional Neural Network with Bicubic Spline Interpolation for Sound Field Estimation
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DOI：
10.1109/iwaenc53105.2022.9914792
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发表时间：
2022-07
期刊：
影响因子：
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通讯作者：
Kazuhide Shigemi;Shoichi Koyama;Tomohiko Nakamura;H. Saruwatari
中科院分区：
文献类型：
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作者：
Kazuhide Shigemi;Shoichi Koyama;Tomohiko Nakamura;H. Saruwatari
提出了一种基于样条插值的物理信息卷积神经网络（PICNN）声场估计方法。大多数声场估计方法都是基于波函数展开，使估计函数满足亥姆霍兹方程。然而，这些方法仅依赖于物理性质;因此，当测量次数较少时，它们的准确性显著降低。最近基于神经网络的学习方法在训练数据可用时从稀疏测量进行估计方面具有优势。然而，由于没有考虑物理特性，估计的函数可能是物理上不可行的解决方案。我们提出了PICNN的声场估计问题的应用，通过使用损失函数，惩罚偏离亥姆霍兹方程。由于CNN的输出是空间离散的压力分布，因此很难直接计算亥姆霍兹方程损失函数。因此，我们将双三次样条插值的PICNN框架。实验结果表明，该方法可以从稀疏测量中获得准确的物理可行的估计。
A sound field estimation method based on a physics-informed convolutional neural network (PICNN) using spline interpolation is pro-posed. Most of the sound field estimation methods are based on wavefunction expansion, making the estimated function satisfy the Helmholtz equation. However, these methods rely only on physical properties; thus, they suffer from a significant deterioration of accuracy when the number of measurements is small. Recent learning-based methods based on neural networks have advantages in esti-mating from sparse measurements when training data are available. However, since physical properties are not taken into consideration, the estimated function can be a physically infeasible solution. We propose the application of PICNN to the sound field estimation problem by using a loss function that penalizes deviation from the Helmholtz equation. Since the output of CNN is a spatially discretized pressure distribution, it is difficult to directly evaluate the Helmholtz-equation loss function. Therefore, we incorporate bicubic spline interpolation in the PICNN framework. Experimental results indicated that accurate and physically feasible estimation from sparse measurements can be achieved with the proposed method.