The paper addresses the challenge of handling distribution shifts in dynamic graphs, which are inherent due to various uncontrollable factors. Existing methods primarily focus on time domain shifts, but this paper introduces the concept of spectral domain shifts, which are often unobservable in the time domain but observable in the spectral domain. The authors propose Spectral Invariant Learning for Dynamic Graphs under Distribution Shifts (SILD), a novel method that captures and utilizes invariant and variant spectral patterns to handle distribution shifts. SILD uses a dynamic graph neural network (DyGNN) with Fourier transform to obtain ego-graph trajectory spectrums, a disentangled spectrum mask to filter graph dynamics from different frequency components, and an invariant spectral filtering mechanism to discover and exploit invariant patterns. Experimental results on synthetic and real-world datasets demonstrate that SILD outperforms state-of-the-art baselines in both node classification and link prediction tasks under distribution shifts. The paper also includes theoretical analyses and ablation studies to validate the effectiveness of each component of SILD.The paper addresses the challenge of handling distribution shifts in dynamic graphs, which are inherent due to various uncontrollable factors. Existing methods primarily focus on time domain shifts, but this paper introduces the concept of spectral domain shifts, which are often unobservable in the time domain but observable in the spectral domain. The authors propose Spectral Invariant Learning for Dynamic Graphs under Distribution Shifts (SILD), a novel method that captures and utilizes invariant and variant spectral patterns to handle distribution shifts. SILD uses a dynamic graph neural network (DyGNN) with Fourier transform to obtain ego-graph trajectory spectrums, a disentangled spectrum mask to filter graph dynamics from different frequency components, and an invariant spectral filtering mechanism to discover and exploit invariant patterns. Experimental results on synthetic and real-world datasets demonstrate that SILD outperforms state-of-the-art baselines in both node classification and link prediction tasks under distribution shifts. The paper also includes theoretical analyses and ablation studies to validate the effectiveness of each component of SILD.