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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2026
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| Accès en ligne: | https://arxiv.org/abs/2605.10154 |
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| _version_ | 1866916000175226880 |
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| author | Lu, Xiaoxiao Yuan, Ye Shi, Jiahao |
| author_facet | Lu, Xiaoxiao Yuan, Ye Shi, Jiahao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10154 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Lu, Xiaoxiao Yuan, Ye Shi, Jiahao Machine Learning 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. |
| title | Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.10154 |