PINOT: Partition-Invariant Neural Operator Transformer for Flexible Latent Tokens

To reduce computational cost of global processing, several recent neural operators compress physical observations into a smaller set of latent tokens. Using fewer tokens lowers computation, but excessive compression can discard local spatial information, creating a trade-off between predictive accuracy and efficiency. It is therefore desirable to flexibly adapt the partitioning of physical observations into latent tokens according to the problem. This flexibility is particularly useful for complex geometries and nonuniform discretizations, where geometry, observation density, and local spatial variation can differ substantially across regions, making a fixed latent configuration inefficient. However, existing latent-token-based neural operators typically rely on prescribed latent configurations and do not explicitly ensure consistency under changes in latent tokenization. We introduce PINOT, a Partition-Invariant Neural Operator Transformer for flexible latent partitioning. PINOT uses patchwise scale-normalized polynomial coefficients for patch-scale-consistent latent tokens while preserving higher-order local information. Measure-weighted attention further makes global processing consistent with changes in patch density by accounting for the physical measure represented by each token. We theoretically establish partition and discretization consistency together with local expressivity of PINOT. Experiments show that PINOT generalizes to unseen patch resolutions and preserves substantially more spatial information with far fewer latent tokens. Based on these properties, PINOT demonstrates strong predictive performance against representative neural operator competitors, achieving the lowest error on all benchmarks with nonuniform discretizations.