mlsanityData to 7 Oct 2026

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems

arXiv 2505.01736 ↗First posted 3 May 2025cs.LG cs.AIcited by 5

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Abstract (arXiv)

Accurately modeling and forecasting complex systems governed by partial differential equations (PDEs) is crucial in various scientific and engineering domains. However, traditional numerical methods struggle in real-world scenarios due to incomplete or unknown physical laws. Meanwhile, machine learning approaches often fail to generalize effectively when faced with scarce observational data and the challenge of capturing local and global features. To this end, we propose the Physics-encoded Spectral Attention Network (PeSANet), which integrates local and global information to forecast complex systems with limited data and incomplete physical priors. The model consists of two key components: a physics-encoded block that uses hard constraints to approximate local differential operators from limited data, and a spectral-enhanced block that captures long-range global dependencies in the frequency domain. Specifically, we introduce a novel spectral attention mechanism to model inter-spectrum relationships and learn long-range spatial features. Experimental results demonstrate that PeSANet outperforms existing methods across all metrics, particularly in long-term forecasting accuracy, providing a promising solution for simulating complex systems with limited data and incomplete physics.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 33 of its 42 references that are in the map. First posted on arXiv 3 May 2025.

Builds on

33 of 42 references.

References · 33

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21 more
  1. 2021Factorized Fourier Neural Operatorscited by 237
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 3.

5 papers.

  1. 2025Spectral-inspired Operator Learning with Limited Data and Unknown Physicscited by 1
  2. 2025Stable spectral neural operator for learning stiff PDE systems from limited datacited by 0
  3. 2026PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamicscited by 0
  4. 2026Large language models for partial differential equation workflowscited by 0
  5. 2026From Points to Edges: Edge-Conditioned Spectral Operators for Physics-Sensitive PDE Learningcited by 0