RecFNO：一种基于傅立叶神经算子的分辨率不变流场和热场重建方法
RecFNO: a resolution-invariant flow and heat field reconstruction method from sparse observations via Fourier neural operator
摘要：
完整状态感知是支持物理系统监测、分析和设计的重要技术，其挑战之一是从稀疏观测中恢复全局场。深度神经网络以其出色的逼近能力在数据驱动的流场和热场重构研究中具有广泛的应用前景。然而，受网络结构的限制，现有的研究大多学习有限维空间的重建映射，对输出的可变分辨率的可移植性差。在本文中，我们扩展了新的范式的神经操作员，并提出了一个端到端的物理场重建方法，具有良好的性能和网格可移植性命名为RecFNO。该方法旨在学习从稀疏观测到无限维空间中的流场和热场的映射，从而具有更强的非线性拟合能力和分辨率不变特性。首先，根据不同的使用场景，我们开发了三种类型的嵌入来建模稀疏观测输入：MLP，掩码和Voronoi嵌入。MLP嵌入有利于更稀疏的输入，而其他受益于空间信息的保护，并随着观测数据的增加表现得更好。然后，我们采用堆叠的傅里叶层在傅里叶空间中重建物理场，通过傅里叶模式叠加将整个恢复场正则化。该方法利用无限维空间的算子，获得了较高的精度和较好的网格间分辨率传递性。对流体力学和热学问题的实验表明，该方法在大多数情况下优于现有的基于POD和基于CNN的方法，并具有实现zero-shot超分辨率的能力。
英文摘要：
Perception of the full state is an essential technology to support the monitoring, analysis, and design of physical systems, one of whose challenges is to recover global field from sparse observations. Well-known for brilliant approximation ability, deep neural networks have been attractive to data-driven flow and heat field reconstruction studies. However, limited by network structure, existing researches mostly learn the reconstruction mapping in finite-dimensional space and has poor transferability to variable resolution of outputs. In this paper, we extend the new paradigm of neural operator and propose an end-to-end physical field reconstruction method with both excellent performance and mesh transferability named RecFNO. The proposed method aims to learn the mapping from sparse observations to flow and heat field in infinite-dimensional space, contributing to a more powerful nonlinear fitting capacity and resolution-invariant characteristic. Firstly, according to different usage scenarios, we develop three types of embeddings to model the sparse observation inputs: MLP, mask, and Voronoi embedding. The MLP embedding is propitious to more sparse input, while the others benefit from spatial information preservation and perform better with the increase of observation data. Then, we adopt stacked Fourier layers to reconstruct physical field in Fourier space that regularizes the overall recovered field by Fourier modes superposition. Benefiting from the operator in infinite-dimensional space, the proposed method obtains remarkable accuracy and better resolution transferability among meshes. The experiments conducted on fluid mechanics and thermology problems show that the proposed method outperforms existing POD-based and CNN-based methods in most cases and has the capacity to achieve zero-shot super-resolution.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
