365 citations · 677 across the 17 of their papers we have counts for
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math.NA2020★ 3 cited
Discovery of Governing Equations with Recursive Deep Neural Networks
Jia Zhao, Jarrod Mau
Model discovery based on existing data has been one of the major focuses of mathematical modelers for decades. Despite tremendous achievements of model identification from adequate…
math.NA2020★ 32 cited
Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks
Colby L. Wight, Jia Zhao
Phase field models, in particular, the Allen-Cahn type and Cahn-Hilliard type equations, have been widely used to investigate interfacial dynamic problems. Designing accurate, effi…
math.NA2020★ 1 cited
Discovering Phase Field Models from Image Data with the Pseudo-spectral Physics Informed Neural Networks
Jia Zhao
In this paper, we introduce a new deep learning framework for discovering the phase field models from existing image data. The new framework embraces the approximation power of phy…