Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators

• URL: http://arxiv.org/abs/2605.10154v1
• Date: Mon, 11 May 2026 08:00:42 GMT
• Title: Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators
• Abstract summary: We propose a neural forecasting framework that reformulates PDE rollout as learning a Structured Spectral Propagator (SSP) in a propagation-oriented latent space.<n>SSP significantly outperforms state-of-the-art baselines, reducing relative $L$ errors by up to 48.9% and exhibiting improved stability in temporal extrapolation beyond the supervised horizon.
• Score: 5.407057882221537
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Long-horizon forecasting of time-dependent partial differential equations (PDEs) is critical for characterizing the sustained evolution of physical systems. While neural operators have emerged as efficient surrogates, they typically learn implicit finite-time transitions from discrete observations. When deployed autoregressively, such propagators often suffer from rapid error accumulation and dynamic drift. To address this, we propose a neural forecasting framework that reformulates PDE rollout as learning a Structured Spectral Propagator (SSP) in a propagation-oriented latent space. Following an analysis-propagation-synthesis design, our framework: (i) maps physical states into a shared, time-consistent spatial representation; (ii) projects this space into a compact propagation state to isolate recurrent dynamics from fine-grained spatial details, thereby decoupling reconstruction fidelity from rollout regularity; and (iii) evolves retained spectral modes using a frequency-conditioned linear backbone complemented by a nonlinear spectral closure to account for truncated interactions. This explicit structuring endows the propagator with a strong inductive bias for coherent modal evolution. Extensive experiments demonstrate that SSP significantly outperforms state-of-the-art baselines, reducing relative $L_2$ errors by up to 48.9% and exhibiting improved stability in temporal extrapolation beyond the supervised horizon.

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