We introduce an optimized physics-informed neural network (PINN) trained to solve the problem of identifying and characterizing a surface breaking crack in a metal plate. PINNs are neural networks that can combine data and physics in the learning process by adding the residuals of a system of Partial Differential Equations to the loss function. Our PINN is supervised with realistic ultrasonic surface acoustic wave data acquired at a frequency of 5 MHz. The ultrasonic surface wave data is represented as a surface deformation on the top surface of a metal plate, measured by using the method of laser vibrometry. The PINN is physically informed by the acoustic wave equation and its convergence is sped up using adaptive activation functions. The adaptive activation function uses a scalable hyperparameter in the activation function, which is optimized to achieve best performance of the network as it changes dynamically the topology of the loss function involved in the optimization process. The usage of adaptive activation function significantly improves the convergence, notably observed in the current study. We use PINNs to estimate the speed of sound of the metal plate, which we do with an error of 1\%, and then, by allowing the speed of sound to be space dependent, we identify and characterize the crack as the positions where the speed of sound has decreased. Our study also shows the effect of sub-sampling of the data on the sensitivity of sound speed estimates. More broadly, the resulting model shows a promising deep neural network model for ill-posed inverse problems.

中文翻译：

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用于表面断裂裂纹超声无损量化的物理信息神经网络

我们引入了经过优化的物理信息神经网络 (PINN)，以解决识别和表征金属板表面断裂裂纹的问题。PINN 是神经网络，它可以通过将偏微分方程系统的残差添加到损失函数中，在学习过程中结合数据和物理。我们的 PINN 受到以 5 MHz 频率采集的真实超声表面声波数据的监督。超声波表面波数据表示为金属板顶面的表面变形，使用激光测振法测量。PINN 由声波方程物理通知，并且使用自适应激活函数加速其收敛。自适应激活函数在激活函数中使用可扩展的超参数，它经过优化以实现网络的最佳性能，因为它会动态改变优化过程中涉及的损失函数的拓扑结构。自适应激活函数的使用显着提高了收敛性，在当前研究中观察到这一点。我们使用 PINN 来估计金属板的声速，我们以 1\% 的误差进行估算，然后，通过允许声速与空间相关，我们将裂纹识别并表征为声速降低了。我们的研究还显示了数据子采样对声速估计灵敏度的影响。更广泛地说，由此产​​生的模型显示了一个有前途的深度神经网络模型，用于不适定逆问题。