5 papers
On the dichotomy of -walk dimensions on metric measure spaces II
Meng Yang
On a volume doubling metric measure space endowed with a family of -energies such that the Poincaré inequality and the capacity upper bound with -walk dimension hold, f…
Unconditionally Stable, Variable Step DLN Methods for the Allen-Cahn Active Fluid Model: A Divergence-free Preserving Approach
Nan Zheng, Wenlong Pei, Qingguang Guan +1
This paper addresses the divergence-free mixed finite element method (FEM) for nonlinear fourth-order Allen-Cahn phase field coupled active fluid equations. By introducing an auxil…
A Divergence-free Preserving Mixed Finite Element Method for Thermally Driven Active Fluid Model
Nan Zheng, Qingguang Guan, Wenlong Pei +1
In this report, we propose a divergence-free preserving mixed finite element method (FEM) for the system of nonlinear fourth-order thermally driven active fluid equations. By intro…
How Can Deep Neural Networks Fail Even With Global Optima?
Qingguang Guan
Fully connected deep neural networks are successfully applied to classification and function approximation problems. By minimizing the cost function, i.e., finding the proper weigh…
Hybrid PDE-Deep Neural Network Model for Calcium Dynamics in Neurons
Abel Gurung, Qingguang Guan
Traditionally, calcium dynamics in neurons are modeled using partial differential equations (PDEs) and ordinary differential equations (ODEs). The PDE component focuses on reaction…