Learning Green's Functions of Linear Reaction-Diffusion Equations with Application to Fast Numerical Solver

Partial differential equations are often used to model various physical phenomena, such as heat diffusion, wave propagation, fluid dynamics, elasticity, electrodynamics and image processing, and many analytic approaches or traditional numerical methods have been developed and widely used for their solutions. Inspired by rapidly growing impact of deep learning on scientific and engineering research, in this paper we propose a novel neural network, GF-Net, for learning the Green's functions of linear reaction-diffusion equations in an unsupervised fashion. The proposed method overcomes the challenges for finding the Green's functions of the equations on arbitrary domains by utilizing physics-informed approach and the symmetry of the Green's function. As a consequence, it particularly leads to an efficient way for solving the target equations under different boundary conditions and sources. We also demonstrate the effectiveness of the proposed approach by experiments in square, annular and L-shape domains

Effect of Annealing Time on the Cyclic Characteristics of Ceramic Oxide Thin Film Thermocouples

Oxide thin film thermocouples (TFTCs) are widely used in high-temperature environment measurements and have the advantages of good stability and high thermoelectric voltage. However, different annealing processes affect the performance of TFTCs. This paper studied the impact of different annealing times on the cyclic characteristics of ceramic oxide thin film thermocouples. ITO/In2O3 TFTCs were prepared on alumina ceramics by a screen printing method, and the samples were annealed at different times. The microstructure of the ITO film was studied by scanning electron microscopy (SEM), X-ray diffraction (XRD), and X-ray photoelectron spectroscopy (XPS). The results show that when the annealing temperature is fixed, the stability of the thermocouple is worst when it is annealed for 2 h. Extending the annealing time can improve the properties of the film, increase the density, slow down oxidation, and enhance the thermal stability of the thermocouple. The thermal cycle test results show that the sample can reach five temperature rise and fall cycles, more than 50 h, and can meet the needs of stable measurement in high temperature and harsh environments