SPEAR: A Spectral-Disentangled MoE Neural Operator with Knowledge-Guided Expert Aggregation for Large-Scale PDE Pretraining

arXiv:2610.03265v1 Announce Type: cross Abstract: Large-scale pre-training has improved the generalization of neural operators across diverse PDEs. However, existing PDE foundation models still struggle with heterogeneous dynamics, where shared representations may cause knowledge interference, while mixture-of-experts (MoE) architectures suffer from increasing expert redundancy. We propose SPEAR, a spectral-disentangled MoE neural operator with knowledge-guided expert aggregation for large-scale PDE pre-training. SPEAR decouples latent features into low- and high-frequency components, enabling shared modeling of transferable dynamics and specialized learning of PDE-specific patterns. To address expert redundancy, we design a knowledge-guided expert aggregation strategy that measures expert similarity from dataset-specific learned knowledge and routing preferences, enabling the identification and consolidation of similar experts. Experiments on twelve PDE datasets and multiple downstream benchmarks demonstrate superior performance in pre-training, fine-tuning, and transfer learning. Furthermore, our aggregation strategy reduces the number of experts by 50\% while maintaining or improving prediction accuracy, achieving a balance between model efficiency and generalization for PDE foundation models.

Abstract:Large-scale pre-training has improved the generalization of neural operators across diverse PDEs. However, existing PDE foundation models still struggle with heterogeneous dynamics, where shared representations may cause knowledge interference, while mixture-of-experts (MoE) architectures suffer from increasing expert redundancy. We propose SPEAR, a spectral-disentangled MoE neural operator with knowledge-guided expert aggregation for large-scale PDE pre-training. SPEAR decouples latent features into low- and high-frequency components, enabling shared modeling of transferable dynamics and specialized learning of PDE-specific patterns. To address expert redundancy, we design a knowledge-guided expert aggregation strategy that measures expert similarity from dataset-specific learned knowledge and routing preferences, enabling the identification and consolidation of similar experts. Experiments on twelve PDE datasets and multiple downstream benchmarks demonstrate superior performance in pre-training, fine-tuning, and transfer learning. Furthermore, our aggregation strategy reduces the number of experts by 50\% while maintaining or improving prediction accuracy, achieving a balance between model efficiency and generalization for PDE foundation models.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2610.03265 [cs.LG]

(or arXiv:2610.03265v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.03265 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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SPEAR: A Spectral-Disentangled MoE Neural Operator with Knowledge-Guided Expert Aggregation for Large-Scale PDE Pretraining

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