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

Large-scale pre-training has improved the generalization of neural operators across diverse PDEs. However, existing PDE foundation models still face heterogeneous dynamics, where shared representations may cause knowledge interference and MoE architectures may introduce expert redundancy. We propose SPEAR, a spectral-disentangled MoE neural operator with knowledge-guided expert aggregation for large-scale PDE pre-training. SPEAR separates latent features into low- and high-frequency components, enabling shared modeling of transferable dynamics and specialized learning of PDE-specific patterns. To reduce redundancy, we further introduce a knowledge-guided aggregation strategy that measures expert similarity using dataset-specific knowledge and routing preferences, and consolidates similar experts. Experiments on twelve PDE datasets and multiple downstream benchmarks demonstrate strong performance in pre-training, fine-tuning, and transfer learning. Our aggregation strategy further reduces the number of experts by 50% while maintaining or improving prediction accuracy, balancing efficiency and generalization.