This paper launches a thorough discussion on the locality of local neural
operator (LNO), which is the core that enables LNO great flexibility on varied
computational domains in solving transient partial differential equations
(PDEs). We investigate the locality of LNO by looking into its receptive field
and receptive range, carrying a main concern about how the locality acts in LNO
training and applications. In a large group of LNO training experiments for
learning fluid dynamics, it is found that an initial receptive range compatible
with the learning task is crucial for LNO to perform well. On the one hand, an
over-small receptive range is fatal and usually leads LNO to numerical
oscillation; on the other hand, an over-large receptive range hinders LNO from
achieving the best accuracy. We deem rules found in this paper general when
applying LNO to learn and solve transient PDEs in diverse fields. Practical
examples of applying the pre-trained LNOs in flow prediction are presented to
confirm the findings further. Overall, with the architecture properly designed
with a compatible receptive range, the pre-trained LNO shows commendable
accuracy and efficiency in solving practical cases.

本文讨论了局部神经算子（LNO）的局部性问题，探究了其感受野和感受范围，并发现初始感受范围对于 LNO 良好表现至关重要。通过大量实验验证，本文得出了适用于不同领域的局部神经算子学习瞬态偏微分方程的普适规律，并通过实际案例验证了预训练的 LNO 在流体预测中的高准确性和高效率表现。