MATHEMATICAL SCIENCES

Progress has been made in the research of fusion physical neural networks


The fluid data obtained through experiments is usually sparse or incomplete, and how to use imperfect flow field data to extract high-resolution data or characteristic information of the flow field is an important problem in the field of experimental fluid mechanics and is of great significance for high-precision data acquisition. Traditional methods mostly use the method of directly solving the NS equation, using data assimilation, embedding sparse flow field data for solving or prediction, such traditional methods require a lot of upfront code work, and require fine meshing supplemented by high-precision solving, and low flexibility. Physics-Informed Neural Networks (PINNs) have gained a lot of applications in related fields because they can fuse data and equations without dividing elaborate meshes during solving, and have obtained exciting results in laminar flow and low Reynolds number flow. However, for the strong nonlinear hydrodynamic equations and complex high Reynolds number flow, PINNs cannot be effectively solved at this stage, and it is urgent to improve the engineering practicality.

Recently, the fluid-structure interaction and numerical computing team of the Institute of Mechanics has made progress in the practical research of fluid mechanics by fusing physical neural networks. Faced with the problems of flow field reconstruction and flow field super-resolution solving, firstly, the sparse measurement problem in the simulation project is simulated, and the flow field reconstruction ability of the PINNs method under different spatiotemporal sparsity data and locally missing data is studied for the flow of low Reynolds number cylinders, so as to realize the efficient flow field reconstruction under spatial sparseness 1% and spatial extreme data loss. Furthermore, aiming at the problem of flow field feature extraction, a PINN-POD method enhanced by PINNs is proposed, which makes full use of the ability of PINNs to reconstruct the complete flow field from sparse data, effectively reduces the dependence of traditional POD on high spatiotemporal resolution data, and realizes the accurate extraction of the structural features of the flow field from a small number of long-term measurement data through the time domain decomposition strategy. Finally, aiming at the common problem of long training time and low fitting accuracy of high Reynolds number flow in large spatiotemporal domain PINNs, the research team proposes a parallel computing framework based on overlapping domain spatiotemporal decomposition, and integrates RANS equations to assist the design of spatiotemporal overlapping domain decomposition, so as to achieve efficient and accurate solution for higher Reynolds number flows.

The relevant research results were published in Acta Mechanica Sinica (2023, 39(3): 322302), Physics of Fluids (2023, 35, 037119) and Physics of Fluids (2023, 35, 065141), with Associate Professor Sun Zhenxu as the corresponding author, PhD student Chang Yan and Master student Shengfeng Xu as the first authors. The work on the spatiotemporal parallel framework for PINNs was selected as a featured article by the editor-in-chief of Physics of Fluids. Some of the results were exchanged by Sun Zhenxu at the 4th National Symposium on Intelligent Fluid Mechanics, and the research work was supported by the National Key R&D Program of China (2022YFB2603400), the International Partnership Program of the Chinese Academy of Sciences (025GJHZ2022118FN) and the major project of the Science and Technology Research and Development Program of China Railway Group (K2023J047). (Source: Institute of Mechanics, Chinese Academy of Sciences)

Related paper information:https://doi.org/10.1007/s10409-022-22302-x

https://doi.org/10.1063/5.0138287

https://doi.org/10.1063/5.0155087

Figure 1 Flow field reconstruction characteristics of PINNs under limit data

Figure 2 Comparison of traditional POD modalities and PINN-POD modalities

Figure 3 Spatial-temporal parallel framework design for STPINNs

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