Complex-Valued Physics-Informed Neural Network for Near-Field Acoustic Holography

We present a novel approach to Near-field Acoustic Holography (NAH) with the introduction of the Complex-Valued Kirchhoff-Helmholtz Convolutional Neural Network (CV-KHCNN). Our study focuses on analyzing Complex-Valued Neural Networks (CVNNs) in the application of NAH scenario. We compare the performance between CV-KHCNN and its equivalent Real-Valued Neural Networks (RVNNs). Moreover, different complex activation functions are evaluated for CV-KHCNN. The results emphasize the effectiveness of CVNNs in tackling NAH challenges and highlight the suitability of Cardioid as the activation function for CVNNs. This discovery underscores the promising contributions of CVNNs to the field of NAH. T-distributed Stochastic Neighbor Embedding (t-SNE) is further adopted to visualize the features of the embedding layer. The results show that even without prior knowledge of the vibrations, CV-KHCNN demonstrates the capability to distinguish between different boundary conditions (BCs) and mode shapes.