This thesis addresses the critical challenge of “sparse data and scarce knowledge” in developing a generic Prognostics and Health Management (PHM) model. A comprehensive literature review highlights the efficacy of hybrid models combining physics-based modeling with machine learning, focusing on Physics-Informed Machine Learning (PIML) and Self-Supervised Learning (SSL) for enhanced learning from unlabeled data. Thereby, this thesis contributes to advancing both PIML and SSL theories and their practical applications in PHM.The first contribution is developing a generic architectural and learning strategy solution for PIML. Various informed approaches are analyzed, and the mimetic theory is proposed to design flexible, physically consistent neurons and interlayer connections. This novel approach leads to the development of the Rotor Finite Elements Mimetic Neural Network (RFEMNN), which mimics rotor finite element-based dynamics to adjust weight distribution and data flow within the neural network. RFEMNN effectively localizes and recognizes compound faults across multiple rotor structures and conditions. To enhance RFEMNN's few-shot diagnostic capability, constraint projection theory and a reinforcement learning strategy are proposed, aligning the learning process with physics. A generic PIML architecture with parallel, independent PI and data-driven branches is proposed, involving a three-stage training process: pre-training the data-driven branch, freezing it to train the PI branch, and joint training of both branches. This method combines optimized local branches into a comprehensive global model, ensuring the PIML model's performance exceeds original data-driven models under spare data context. Moreover, the solid electrolyte interphase growth-informed Dilated CNN model using this approach showcases its superiority, surpassing leading models in predicting lithium-ion battery RUL with small-cycle data.The second contribution is developing an innovative SSL strategy for unlabeled data learning, introducing a Siamese CNN-LSTM model with a custom contrastive loss function. This model extracts robust feature representations by maximizing differences in the same samples presented in varied sequential orders. Variants of downstream tasks are proposed as intermediate objectives in SSL pretext learning, integrating downstream structures into the pre-training model to align representations with downstream requirements. Under this strategy, the proposed Siamese CNN-LSTM excels at predicting RUL on PRONOSTIA-bearing dataset and remains stable even as training data sparsity increases.The final contribution extends PIML concepts for active knowledge discovery on unlabeled data and integrates SSL into the second phase of PIML's three-step training, utilizing both labeled and unlabeled data. A novel Liquid PI structure and an end-to-end Liquid PI-CNN-Selective state space model (CNN-SSM) are developed. The Liquid PI design introduces gated neurons and liquid interlayer connections that adapt dynamically, acquiring physics knowledge through an optimized search within a predefined operator pool. Demonstrated in torque monitoring of robot manipulators, this approach efficiently discovers knowledge using basic physical operators and dynamic weights from unlabeled data. The Liquid PI CNN-SSM processes variable-length input sequences without signal preprocessing, optimizing resources by requiring only 600 KB to handle 23.9 GB of data. It achieves state-of-the-art performance in mixed prognostic tasks, including bearing degradation, tool wear, battery aging, and CFRP tube fatigue, showcasing the originality and versatility of the proposed approach.Future work will apply PHM-specific scaling laws and train on extensive synthetic and industry datasets to build a cross-modal macro-model. It could integrate diagnostic-prognostic capabilities with infinite sequence length processing, continuing to transform PHM methodologies and solutions.