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

2026-05-15

AI Summary

This work addresses the “phase amnesia” problem in non-stationary time series forecasting—caused by the unrealistic assumption of static historical dynamics—by proposing the first plug-and-play framework that integrates physical priors. Grounded in three key physical assumptions—Wold decomposition, dynamic phase evolution, and heteroscedastic manifold generation—the method adopts a “decouple–evolve–simulate” paradigm. It enhances robustness through phase-anchored decoupling, Phase Router–based trajectory generation, and a statistical-aware mixture (SAM) mechanism, all built upon an MLP backbone guided by physics-informed inductive biases. By explicitly modeling phase dynamics, the approach overcomes reliance on static assumptions and demonstrates that well-designed inductive biases outweigh architectural complexity. Evaluated on twelve real-world benchmarks, it achieves state-of-the-art or highly competitive performance, underscoring the critical role of physics-guided inductive bias in non-stationary forecasting.

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.

Problem

• non-stationary time series forecasting
• phase amnesia
• distribution shift
• global context evolution

Innovation

• non-stationary time series
• physics-informed forecasting
• phase evolution
• disentangled representation
• out-of-distribution robustness