Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks
نویسندگان
چکیده
Phase field models, in particular, the Allen-Cahn type and Cahn-Hilliard equations, have been widely used to investigate interfacial dynamic problems. Designing accurate, efficient, stable numerical algorithms for solving phase models has an active decades. In this paper, we focus on using deep neural network design automatic solver equations by proposing improved physics informed (PINN). Though PINN embraced many differential equation problems, find a direct application of phase-field won't provide accurate solutions cases. Thus, propose various techniques that add approximation power PINN. As major contribution embrace adaptive idea both space time introduce sampling strategies, such are able improve efficiency accuracy equations. addition, no restriction explicit form PDEs, making it applicable wider class PDE shedding light approximations other PDEs general.
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ژورنال
عنوان ژورنال: Communications in Computational Physics
سال: 2021
ISSN: ['1991-7120', '1815-2406']
DOI: https://doi.org/10.4208/cicp.oa-2020-0086