On the locality of local neural operator in learning fluid dynamics

Abstract

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.

References in corpus (15)

• Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
• DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
• Gaussian Error Linear Units (GELUs)
• Solving high-dimensional partial differential equations using deep learning
• hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition
• Learning data driven discretizations for partial differential equations
• CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Method
• Data-driven prediction of unsteady flow fields over a circular cylinder using deep learning
• PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs
• Physics-Informed Neural Operator for Learning Partial Differential Equations
• Deep transfer operator learning for partial differential equations under conditional shift
• Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loads
• Sequential Deep Operator Networks (S-DeepONet) for Predicting Full-field Solutions Under Time-dependent Loads
• Bayesian Physics Informed Neural Networks for Data Assimilation and Spatio-Temporal Modelling of Wildfires
• Stochastic projection based approach for gradient free physics informed learning

Cited by in corpus (2)

• Predictions of Transient Vector Solution Fields with Sequential Deep Operator Network
• Uncertainty quantification and stability of neural operators for prediction of three-dimensional turbulence