On the locality of local neural operator in learning fluid dynamics
Ximeng Ye Hongyu Li Jingjie Huang Guoliang Qin
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.