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We propose attention-based modeling of quantities at arbitrary spatial pointsconditioned on related measurements at different locations. Our approach adaptsa transformer-encoder to process measurements and read-out positions together.Attention-based models exhibit excellent performance across domains, whichmakes them an interesting candidate for modeling data irregularly sampled inspace. We introduce a novel encoding strategy that applies the sametransformation to the measurements and read-out positions, after which they arecombined with encoded measurement values instead of relying on two differentmappings.  Efficiently learning input-output mappings from irregularly-spaced data is afundamental challenge in modeling physical phenomena. To evaluate theeffectiveness of our model, we conduct experiments on diverse problem domains,including high-altitude wind nowcasting, two-days weather forecasting, fluiddynamics, and heat diffusion. Our attention-based model consistentlyoutperforms state-of-the-art models, such as Graph Element Networks andConditional Neural Processes, for modeling irregularly sampled data. Notably,our model reduces root mean square error (RMSE) for wind nowcasting, improvingfrom 9.24 to 7.98 and for a heat diffusion task from .126 to .084. Wehypothesize that this superior performance can be attributed to the enhancedflexibility of our latent representation and the improved data encodingtechnique. To support our hypothesis, we design a synthetic experiment thatreveals excessive bottlenecking in the latent representations of alternativemodels, which hinders information utilization and impedes training.

Attention-based Modeling of Physical Systems: Improved Latent Representations