From physics to machine learning and back: Part I - Learning with inductive biases in prognostics and health management (PHM)

Prognostics and Health Management (PHM) is essential for ensuring the safe, reliable, and efficient operation of complex engineered systems by integrating fault detection, diagnostics, and prognostics into a unified framework. While machine learning (ML) has significantly advanced PHM by enabling data-driven decision-making, real-world challenges such as sparse or noisy data, limited labels, and complex degradation dynamics require approaches that go beyond purely data-driven modeling. This review focuses on inductive bias – the integration of prior knowledge, physical laws, and structural assumptions into ML model design – as a foundational mechanism to improve generalization, robustness, and interpretability in PHM. We explore the current state of the art in applying inductive bias to PHM, reviewing a wide range of methods including graph neural networks (relational biases), state-space models and neural ordinary differential equations (temporal biases), signal processing-inspired learning (spectral biases), neural operators (operator biases), causal representation learning (causal biases), and interpretable-by-design models (interpretability biases) through the use of inductive bias. For each method, we discuss its advantages, limitations, and suitability for different PHM tasks, and identify emerging applications where these techniques show strong potential. Furthermore, we examine how ML contributes back to physics understanding through symbolic regression (rediscovering physical laws) and post-hoc interpretation (transparent decision-making), closing the loop between physics understanding and modeling in PHM. By embedding domain knowledge into learning architectures, these approaches help constrain the hypothesis space and promote physically consistent learning, bridging the gap between theoretical modeling and real-world deployment in safety-critical applications. Part II of this review explores observational and learning biases, focusing on how data augmentation, representation, and training strategies shape model behavior and further enhance alignment between machine learning and the physical systems it aims to monitor and manage.