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4 papers · 2 filters
A model-data asymptotic-preserving neural network method based on micro-macro decomposition for gray radiative transfer equations
Hongyan Li, Song Jiang, Wenjun Sun +2
We propose a model-data asymptotic-preserving neural network(MD-APNN) method to solve the nonlinear gray radiative transfer equations(GRTEs). The system is challenging to be simula…
A fully asymptotic preserving decomposed multi-group method for the frequency-dependent radiative transfer equations
Xiaojiang Zhang, Peng Song, Yi Shi +1
The opacity of FRTE depends on not only the material temperature but also the frequency, whose values may vary several orders of magnitude for different frequencies. The gray radia…
Pre-training strategy for solving evolution equations based on physics-informed neural networks
Jiawei Guo, Yanzhong Yao, Han Wang +1
The physics informed neural network (PINN) is a promising method for solving time-evolution partial differential equations (PDEs). However, the standard PINN method may fail to sol…
Energy stability of variable-step L1-type schemes for time-fractional Cahn-Hilliard model
Bingquan Ji, Xiaohan Zhu, Hong-lin Liao
The positive definiteness of discrete time-fractional derivatives is fundamental to the numerical stability (in the energy sense) for time-fractional phase-field models. A novel te…