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We present a computational recognition approach to convert network-like, image-based engineering diagrams into engineering models with which computations of interests, such as CAD modeling, simulation, information retrieval and semantic-aware editing, are enabled. The proposed approach is designed to work on diagrams produced using computer-aided drawing tools or hand sketches, and does not rely on temporal information for recognition. Our approach leverages a Convolutional Neural Network (CNN) as a trainable engineering symbol recognizer. The CNN is capable of learning the visual features of the defined symbol categories from a few user-supplied prototypical diagrams and a set of synthetically generated training samples. When deployed, the trained CNN is applied either to the entire input diagram using a multi-scale sliding window or, where applicable, to each isolated pixel cluster obtained through Connected Component Analysis (CCA). Then the connectivity between the detected symbols are analyzed to obtain an attributed graph representing the engineering model conveyed by the diagram. We evaluate the performance of the approach with benchmark datasets and demonstrate its utility in different application scenarios, including the construction and simulation of control system or mechanical vibratory system models from hand-sketched or camera-captured images, content-based image retrieval for resonant circuits and sematic-aware image editing for floor plans.