MoNo: Multiscale Optimal Transport Neural Operator for Solving PDEs on General Geometries
MoNo uses optimal transport to keep latent tokens balanced instead of letting deeper PDE operator layers collapse.
The paper says existing projection methods can overload some latent tokens while leaving others underused, and that the imbalance worsens across hierarchical latent spaces. Its proposed CoTAP module treats cross-scale assignment as an entropy-regularized optimal transport problem, producing balanced bidirectional projections. The authors argue this makes multiscale neural operators viable on general geometries and improves long-range physical interaction learning. They report stronger prediction performance and computational efficiency than existing state-of-the-art neural operators. ArXiv · AI/CL/LG's note
The paper says existing projection methods can overload some latent tokens while leaving others underused, and that the imbalance worsens across hierarchical latent spaces. Its proposed CoTAP module treats cross-scale assignment as an entropy-regularized optimal transport problem, producing balanced bidirectional projections. The authors argue this makes multiscale neural operators viable on general geometries and improves long-range physical interaction learning. They report stronger prediction performance and computational efficiency than existing state-of-the-art neural operators. ArXiv · AI/CL/LG's note
score 4