Disentangling Attention in Deep Operator Learning: A Controlled Study of Data-Driven and Physics-Informed Architectures

תקציר מקורי באנגליתarXiv:2609.04407v1 Announce Type: new Abstract: Deep neural operators learn mappings between input functions and complete PDE solution fields, enabling forward evaluations of new problem instances orders of magnitude faster than conventional numerical solvers. Attention mechanisms have recently been introduced into neural operators, but most studies change several architectural components at once, making it difficult to identify what actually improves accuracy. This work presents a controlled and systematic study of five deep operator network (DeepONet) variants with distinct attention mechanisms, trained under both data-driven and physics-informed regimes, to isolate the effects of cross-attention, self-attention, tokenization, and attention depth. We evaluate them on a source-driven tran