PULSE: Generative Phase Evolution for Non-Stationary Time Series Forecasting

• URL: http://arxiv.org/abs/2605.16793v2
• Date: Wed, 20 May 2026 12:54:33 GMT
• Title: PULSE: Generative Phase Evolution for Non-Stationary Time Series Forecasting
• Abstract summary: Time series forecasting under non-stationarity faces a fundamental tension between capturing stable representations and adapting to distribution shifts.<n>We formalize non-stationary dynamics through three physical hypotheses: wold decomposition, dynamical phase evolution, and heteroscedastic manifold generation.<n>These principles inspire PULSE, a physics-informed, plug-and-play framework adopting a Disentangle-Evolve--Simulate design philosophy.
• Score: 18.36615425277525
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Time series forecasting under non-stationarity faces a fundamental tension between capturing stable representations and adapting to distribution shifts. Existing methods implicitly rely on static historical assumptions, leading to a critical failure mode we term Phase Amnesia, where models become blind to the evolving global context. To resolve this, we formalize non-stationary dynamics through three physical hypotheses: wold decomposition, dynamical phase evolution, and heteroscedastic manifold generation. These principles inspire PULSE, a physics-informed, plug-and-play framework adopting a Disentangle--Evolve--Simulate design philosophy. Specifically, PULSE utilizes phase-anchored disentanglement to resolve optimization interference caused by dominant trends, employs a Phase Router to actively generate future trajectories, and introduces Statistic-Aware Mixup (SAM) to ensure robustness against out-of-distribution volatility. Empirically, PULSE enables a simple MLP backbone to achieve state-of-the-art or highly competitive performance across 12 real-world benchmarks. This validates that a correct physics-informed inductive bias is far more critical than raw architectural complexity for non-stationary forecasting. The code is available at: https://github.com/Gemost/PULSE.

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