32 citations · 43 across the 6 of their papers we have counts for
10 papers
A Revisit of The Energy Quadratization Method with A Relaxation Technique
Jia Zhao
This letter revisits the energy quadratization (EQ) method by introducing a novel and essential relaxation technique to improve its accuracy and stability. The EQ method has witnes…
Second-order Decoupled Energy-stable Schemes for Cahn-Hilliard-Navier-Stokes equations
Jia Zhao
The Cahn-Hilliard-Navier-Stokes (CHNS) equations represent the fundamental building blocks of hydrodynamic phase-field models for multiphase fluid flow dynamics. Due to the couplin…
A General Framework to Derive Linear, Decoupled and Energy-stable Schemes for Reversible-Irreversible Thermodynamically Consistent Models: Part I Incompressible Hydrodynamic Models
Jia Zhao
In this paper, we present a general numerical platform for designing accurate, efficient, and stable numerical algorithms for incompressible hydrodynamic models that obeys the ther…
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…
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…
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…