MoNo解决了神经算子中token分配不均的痛点，用最优传输做多尺度，PDE求解又快又准，代码也开源了。
MoNo提出了一种新的神经算子架构，通过CoTAP方法将跨空间分配建模为熵正则化最优传输问题，解决了现有可学习投影机制中潜在token分配不均的问题。该方法构建了平衡的双向投影和稳定的潜在空间，支持在一般几何上的多尺度架构。实验表明，MoNo在预测性能和计算效率上均优于现有最先进的神经算子。代码已开源。
MoNo: Multiscale Optimal Transport Neural Operator for Solving PDEs on General Geometries
Transformer-based neural operators have achieved substantial progress in solving Partial Differential Equations (PDEs) by projecting spatial observations into compact latent tokens and learning physical interactions in latent spaces. However, we reveal that existing learnable projection mechanisms cannot ensure stable and balanced assignments from observation points to latent tokens, causing some latent tokens to be over-assigned while others remain underutilized. This limitation further restricts the design of hierarchical architectures, as assignment imbalance is continuously inherited and amplified across latent spaces, eventually causing severe token collapse in deeper spaces. To address these issues, we propose MoNo (Multiscale Optimal Transport Neural Operator), a progressive multiscale neural operator that efficiently solves PDEs on general geometries through stable latent-space construction. At its core is CoTAP (Cross-scale Optimal Transport Assignment and Projection), a novel latent-space construction method that formulates cross-space assignment between adjacent spaces as an entropy-regularized optimal transport problem, thereby constructing balanced bidirectional projections and stable latent spaces. CoTAP also ensures stable information transfer across multiple latent spaces, further enabling multiscale architectures on general geometries, which in turn support more efficient learning of long-range physical interactions. Extensive experiments demonstrate that MoNo outperforms existing state-of-the-art neural operators in both prediction performance and computational efficiency. Code is available at https://github.com/ZijiangY1116/MoNo.