Predicting structural lifetime under cyclic and fatigue loading is a major challenge in computational mechanics, especially for high-cycle fatigue problems in large-scale engineering systems such as aircraft, bridges, and wind turbines. Fatigue damage accumulation, crack initiation, and crack growth critically affect durability, yet direct mechanistic simulations over millions of cycles remain computationally prohibitive. This work introduces a dual-model physics-based machine learning ($\phi$ML) framework to capture both cycle-level fracture behavior and lifetime-scale fatigue evolution. One model predicts damage evolution throughout the full cyclic loading history, while the other operates at the lifetime scale, estimating accumulated damage over chunks of cycles. Both models employ double feed-forward neural networks guided by physical constraints, including energy balance, damage evolution, and degradation laws, ensuring physically consistent, interpretable, and generalizable predictions across unseen materials and loading scenarios. Validation studies demonstrate that the models accurately reproduce nonlinear damage evolution under diverse loading histories and material parameters. The lifetime-scale model enables efficient high-cycle fatigue simulations by serving as a surrogate that jumps over multiple cycles without sacrificing accuracy, even in cases of complex, non-linear damage accumulation. This approach provides computationally efficient, scalable, and interpretable simulations of cyclic damage, enabling safer and more durable designs.