Mixture-of-Experts Operator Transformer for Large-Scale PDEPre-Training

Pre-training has proven effective in addressing data scarcity and performance limitations in solving PDE problems with neural operators. However, challenges remain due to the heterogeneity of PDE datasets in equation types, which leads to high errors in mixed training. Additionally, dense pre-training models that scale parameters by increasing network width or depth incur significant inference costs. To tackle these challenges, we propose a novel Mixture-of-Experts Pre-training Operator Transformer (MoE-POT), a sparse-activated architecture that scales parameters efficiently while controlling inference costs. Specifically, our model adopts a layer-wise router-gating network to dynamically select 4 routed experts from 16 expert networks during inference, enabling the model to focus on equationspecific features. Meanwhile, we also integrate 2 shared experts, aiming to capture common properties of PDE and reduce redundancy among routed experts. The final output is computed as the weighted average of the results from all activated experts.