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Life sciences · Preprint
arXiv · August 10, 2026
Posted before peer review. The findings may change or fail to hold.
This is an unrefereed preprint proposing MoNo, a neural operator architecture for solving PDEs via a novel optimal-transport-based latent-space construction method called CoTAP. The authors claim superior performance and efficiency compared to existing neural operators, but no peer-reviewed validation, quantitative benchmarks, or effect sizes are reported in the source text.
Preprint.
Existing learnable projection mechanisms in transformer-based neural operators suffer from unstable and imbalanced token assignment, leading to token collapse in deeper layers. CoTAP formulates cross-space assignment as an entropy-regularized optimal transport problem to construct balanced bidirectional projections. MoNo claims to outperform existing state-of-the-art neural operators in both prediction performance and computational efficiency (no numerical comparison provided in abstract).
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This is an unrefereed preprint describing a novel computational method for solving PDEs; it reports algorithmic performance but has not undergone peer review.
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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.
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