Deep Wavelet Neural Process: Modeling Stochastic Variation of Non-Euclidean Functional Data for Manufacturing Quality Inference

Modeling and inferring the intricate stochastic variations of the manufacturing quality still remain a significant challenge, especially when dealing with non-Euclidean functional data, which emerge ubiquitous in manufacturing processes. To address this issue, this study proposes the deep wavelet neural process (DWNP), an innovative deep learning model leveraging the exceptional potential of neural processes (NPs) for modeling high-dimensional stochastic variations and the superiority of geometric deep learning in analyzing non-Euclidean functional data, to facilitate typical manufacturing quality inference tasks characterized by non-Euclidean functional data. Three major works have been done in this study. First, the Laplace–Beltrami operator was manipulated and a fast spectral graph wavelet transform was performed to derive a tailored graph wavelet neural network (GWNN), which possesses the ability to capture and decouple complex variation patterns in typical non-Euclidean functional data in manufacturing. Second, based on the theoretical and structural prototype of NPs, the DWNP was derived and built up, exploiting the GWNN to model the stochastic variations of non-Euclidean functional data. Finally, an experiment was conducted on a real automotive manufacturing process to verify the effectiveness and superiority of the proposed DWNP model, in which two typical non-Euclidean functional data types were investigated.