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Research questionWhich attention mechanisms reliably improve DeepONet accuracy across data-driven and physics-informed PDE solving?DeepONet attention designs differ in tokenization, cross-attention, self-attention, fusion, and depth, but studies often change several components simultaneously. This makes it difficult to determine which architectural choices affect accuracy across different PDE problems and training regimes.
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Latest papersRecent research connected to this question, newest first.Disentangling Attention in Deep Operator Learning: A Controlled Study of Data-Driven and Physics-Informed ArchitecturesThe evidence comes from controlled comparisons of five DeepONet variants on transient one-dimensional nonlinear diffusion-reaction and viscous Burgers equations, plus a two-dimensional Poisson heat-conduction problem with heterogeneous sources. The study evaluates both data-driven and physics-informed training, including the accuracy and training-cost effects of attention depth.research paper · Sep 3, 2026
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