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math.NA2022
Bifurcation Analysis Reveals Solution Structures of Phase Field Models
Xinyue Evelyn Zhao, Long-Qing Chen, Wenrui Hao +1
Phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems. Here, we develop a new ana…
math.NA2021★ 2 cited
Two neural-network-based methods for solving obstacle problems
Xinyue Evelyn Zhao, Wenrui Hao, Bei Hu
Two neural-network-based numerical schemes are proposed to solve the classical obstacle problems. The schemes are based on the universal approximation property of neural networks,…
math.NA2020
Convergence analysis of neural networks for solving a free boundary system
Xinyue Evelyn Zhao, Wenrui Hao, Bei Hu
Free boundary problems deal with systems of partial differential equations, where the domain boundaries are apriori unknown. Due to this special characteristic, it is challenging t…