Convolutional embedding for small-data process modeling and extrapolation with application to twin-screw extrusion

Small-data challenges remain prevalent in the process industries, even in the era of big data. During the design phase of a new industrial process, the vast combinations of materials, equipment configurations, and operating conditions often result in insufficient data for each individual setting, making data-driven modeling particularly difficult. For example, in extrusion-process design, only limited samples can be collected for each pairing of operating conditions and screw conFig. urations. Our previous deep embedding network (DEN) could integrate qualitative and quantitative factors but was restricted to screw elements within a predefined set and could not handle unseen types. To overcome this limitation, we propose a convolutional embedding network (CEN) that improves extrapolation capability by integrating diverse sources of information. A convolutional autoencoder is first employed to extract the functional geometric features of screw elements from their images. These features also exist in previously unseen screw types, thereby enabling generalization beyond the training set. These learned representations are then combined with quantitative operating conditions and fed into a feedforward neural network for prediction. Both components are trained jointly in an end-to-end manner to ensure that the learned geometric features reflect their impact on quality variables. A twin-screw extrusion case study demonstrates that CEN achieves satisfactory accuracy under small-data scenarios, including extrapolation to unseen screw elements, while offering improved interpretability through feature visualization.