| Citation: | WANG Yanjia, QIU Lu, ZHU Jianqin. Meshless computing method for thermal conductivity problem based on physical-informed neural networks[J]. Journal of Aerospace Power, 2023, 38（7）：1626-1636 doi: 10.13224/j.cnki.jasp.20220753
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A general framework for solving thermal conductivity problems by physics-informed neural networks (PINNs) was developed and the treatment methods of three-dimensional unsteady problems, initial conditions, three types of boundary conditions, and surface boundaries were described. A one-dimensional thermal conductivity problem was solved by PINNs. The maximum relative error and average relative error between the solution and the theoretical solution were 0.0017% and 0.0011%, respectively. Using a simplified blade thermal conductivity problem as a case study, PINNs was compared with conventional finite element methods and the effects of different network architectures and hyperparameters of PINNs on the results were explored. The results showed that for the thermal con-ductivity problem of a simplified blade, the finite element method solved the problem in 11.7 s and PINNs solved in 8.96 s, with a maximum error of 1.03% and an average error of 0.139%. The internal cold source intensity of the solid blade was adjusted slightly, and the new convergence time was 1.41 s based on the PINNs training convergence, proving that PINNs method has the ability of fast calculation in case of minor change of the design condition.
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