365 citations · 677 across the 17 of their papers we have counts for
18 papers
High-Order Variable-Scaled Energetic Variational Neural Networks for Phase-Field Gradient Flows
Xiaobo Jing, Leiyi Dong, Jia Zhao
In this paper, we develop a high-order variable-scaled energetic variational neural network (VS-EVNN) method for phase-field gradient flows. Each discretization stage uses an updat…
Relaxed Lagrange Multiplier (RLM) Schemes for Phase Field Models Preserving the Relaxed Original Energy Dissipation Law
Xiaobo Jing, Jia Zhao
Phase-field models are typically derived from variational principles for a free-energy functional and are widely used to simulate complex multiphase phenomena in science and engine…
Numerical Approximations of the Allen-Cahn-Ohta-Kawasaki (ACOK) Equation with Modified Physics Informed Neural Networks (PINNs)
Jingjing Xu, Jia Zhao, Yanxiang Zhao
The physics informed neural networks (PINNs) has been widely utilized to numerically approximate PDE problems. While PINNs has achieved good results in producing solutions for many…
A Remark on the Invariant Energy Quadratization (IEQ) Method for Preserving the Original Energy Dissipation Laws
Zengyan Zhang, Yuezheng Gong, Jia Zhao
In this letter, we revisit the IEQ method and provide a new perspective on its ability to preserve the original energy dissipation laws. The invariant energy quadratization (IEQ) m…
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…
The effects of simple density-dependent prey diffusion and refuge in a predator-prey system
Leoncio Rodriguez Quinones, Jia Zhao, Luis Gordillo
We study a spatial (two-dimensional) Rosenzweig-MacArthur model under the following assumptions: prey movement follows a nonlinear diffusion, preys have a refuge zone (…
Arbitrarily High-order Linear Schemes for Gradient Flow Models
Yuezheng Gong, Jia Zhao, Qi Wang
We present a paradigm for developing arbitrarily high order, linear, unconditionally energy stable numerical algorithms for gradient flow models. We apply the energy quadratization…
Arbitrarily High-order Unconditionally Energy Stable Schemes for Thermodynamically Consistent Gradient Flow Models
Yuezheng Gong, Jia Zhao, Qi Wang
We present a systematical approach to developing arbitrarily high order, unconditionally energy stable numerical schemes for thermodynamically consistent gradient flow models that…
Arbitrarily High-order Unconditionally Energy Stable Schemes for Gradient Flow Models Using the Scalar Auxiliary Variable Approach
Yuezheng Gong, Jia Zhao, Qi Wang
In this paper, we propose a novel family of high-order numerical schemes for the gradient flow models based on the scalar auxiliary variable (SAV) approach, which is named the high…
On Power Law Scaling Dynamics for Time-fractional Phase Field Models during Coarsening
Lizhen Chen, Jia Zhao, Hong Wang
In this paper, we study the phase field models with fractional-order in time. The phase field models have been widely used to study coarsening dynamics of material systems with mic…
An Accurate and Efficient Algorithm for The Time-fractional Molecular Beam Epitaxy Model with Slope Selection
Lizhen Chen, Jia Zhao, Waixiang Cao +2
In this paper, we propose a time-fractional molecular beam epitaxy (MBE) model with slope selection and its efficient, accurate, full discrete, linear numerical approximation. The…
Numerical Approximations for a three components Cahn-Hilliard phase-field Model based on the Invariant Energy Quadratization method
Xiaofeng Yang, Jia Zhao, Qi Wang +1
How to develop efficient numerical schemes while preserving the energy stability at the discrete level is a challenging issue for the three component Cahn-Hilliard phase-field mode…
Linear, Second order and Unconditionally Energy stable schemes for The Viscous Cahn-Hilliard Equation with hyperbolic relaxation using the invariant energy quadratization method
Xiaofeng Yang, Jia Zhao
In this paper, we consider numerical approximations for the viscous Cahn-Hilliard equation with hyperbolic relaxation. This type of equations processes energy-dissipative structure…