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

TL;DR

PULSE is a physics-informed framework for non-stationary time series forecasting that improves adaptability and robustness by disentangling phase information and actively modeling future dynamics.

Contribution

It introduces a novel physics-inspired approach with phase-anchored disentanglement, a Phase Router, and Statistic-Aware Mixup, achieving state-of-the-art results with simple models.

Findings

PULSE achieves superior performance across 12 real-world benchmarks.

The framework effectively handles distribution shifts and out-of-distribution volatility.

A simple MLP backbone suffices when combined with PULSE's inductive biases.

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.