Smart manufacturing is a revolutionary domain integrating advanced sensing technology, machine learning methods, and the industrial internet of things (IIoT). The development of sensing technology provides large amounts and various types of data (e.g., profile, image, point cloud, etc.) to describe each stage of a manufacturing process. The machine learning methods have the advantages of efficiently and effectively processing and fusing large-scale datasets and demonstrating outstanding performance in different tasks (e.g., diagnosis, monitoring, etc.). Despite the advantages of incorporating machine learning methods into smart manufacturing, there are some widely existing concerns in practice: (1) Most of the edge devices in the manufacturing system only have limited memory space and computational capacity; (2) Both the performance and interpretability of the data analytics method are desired; (3) The connection to the internet exposes the manufacturing system to cyberattacks, which decays the trustiness of data, models, and results. To address these limitations, this dissertation proposed systematic engineering-driven machine learning methods to improve the system intelligence for smart manufacturing. The contributions of this dissertation can be summarized in three aspects. First, tensor decomposition is incorporated to approximately compress the convolutional (Conv) layer in Deep Neural Network (DNN), and a novel layer is proposed accordingly. Compared with the Conv layer, the proposed layer significantly reduces the number of parameters and computational costs without decaying the performance. Second, a physics-informed stochastic surrogate model is proposed by incorporating the idea of building and solving differential equations into designing the stochastic process. The proposed method outperforms pure data-driven stochastic surrogates in recovering system patterns from noised data points and exploiting limited training samples to make accurate predictions and conduct uncertainty quantification. Third, a Wasserstein-based out-of-distribution detection (WOOD) framework is proposed to strengthen the DNN-based classifier with the ability to detect adversarial samples. The properties of the proposed framework have been thoroughly discussed. The statistical learning bound of the proposed loss function is theoretically investigated. The proposed framework is generally applicable to DNN-based classifiers and outperforms state-of-the-art benchmarks in identifying out-of-distribution samples.