Causality-Preserving Domain Generalization via Adaptive Fourier Mixup for RUL Prediction.

Domain generalization (DG) in time series poses significant challenges due to domain shift, particularly under the strict DG setting, where no target domain data are available during training. To address this, we propose AFM-CIR, a unified framework that integrates semantic-similarity-guided Adaptive Fourier Mixing (AFM) with Causality-Inspired Regression (CIR). Specifically, we construct a domain-invariant order-preserving guidance embedding that drives a similarity-based adaptive modulation of amplitude mixing and a bounded shortest-angle phase perturbation, thereby generating label-consistent and causally coherent augmented samples. CIR then enforces invariance and inter-dimensional independence through correlation factorization, while causal sufficiency is encouraged via adversarial masking. We further provide theoretical guarantees of the controllability of phase interventions, supported by mutual information analysis and Lipschitz-spectral norm bounds. Extensive experiments on four widely used benchmark industrial data sets demonstrate that AFM-CIR consistently achieves state-of-the art performance, outperforming strong ERM, general DG, and task-specific DG baselines.