We present a novel class of high-order space-time finite element schemes for the Poisson-Nernst-Planck (PNP) equations. We prove that our schemes are mass conservative, positivity preserving, and unconditionally energy stable for any order of approxi
mation. To the best of our knowledge, this is the first class of (arbitrarily) high-order accurate schemes for the PNP equations that simultaneously achieve all these three properties. This is accomplished via (1) using finite elements to directly approximate the so-called entropy variable instead of the density variable, and (2) using a discontinuous Galerkin (DG) discretization in time. The entropy variable formulation, which was originally developed by Metti et al. [17] under the name of a log-density formulation, guarantees both positivity of densities and a continuous-in-time energy stability result. The DG in time discretization further ensures an unconditional energy stability in the fully discrete level for any approximation order, where the lowest order case is exactly the backward Euler discretization and in this case we recover the method of Metti et al. [17].
Face attribute editing aims to generate faces with one or multiple desired face attributes manipulated while other details are preserved. Unlike prior works such as GAN inversion, which has an expensive reverse mapping process, we propose a simple fe
ed-forward network to generate high-fidelity manipulated faces. By simply employing some existing and easy-obtainable prior information, our method can control, transfer, and edit diverse attributes of faces in the wild. The proposed method can consequently be applied to various applications such as face swapping, face relighting, and makeup transfer. In our method, we decouple identity, expression, pose, and illumination using 3D priors; separate texture and colors by using region-wise style codes. All the information is embedded into adversarial learning by our identity-style normalization module. Disentanglement losses are proposed to enhance the generator to extract information independently from each attribute. Comprehensive quantitative and qualitative evaluations have been conducted. In a single framework, our method achieves the best or competitive scores on a variety of face applications.
A thermodynamically consistent phase-field model is introduced for simulating motion and shape transformation of vesicles under flow conditions. In particular, a general slip boundary condition is used to describe the interaction between vesicles and
the wall of the fluid domain. A second-order accurate in both space and time C0 finite element method is proposed to solve the model governing equations. Various numerical tests confirm the convergence, energy stability, and conservation of mass and surface area of cells of the proposed scheme. Vesicles with different mechanical properties are also used to explain the pathological risk for patients with sickle cell disease.
Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional finite dif
ference and finite elements methods and emerging advancements in machine learning, we propose a sequence deep learning framework called Neural-PDE, which allows to automatically learn governing rules of any time-dependent PDE system from existing data by using a bidirectional LSTM encoder, and predict the next n time steps data. One critical feature of our proposed framework is that the Neural-PDE is able to simultaneously learn and simulate the multiscale variables.We test the Neural-PDE by a range of examples from one-dimensional PDEs to a high-dimensional and nonlinear complex fluids model. The results show that the Neural-PDE is capable of learning the initial conditions, boundary conditions and differential operators without the knowledge of the specific form of a PDE system.In our experiments the Neural-PDE can efficiently extract the dynamics within 20 epochs training, and produces accurate predictions. Furthermore, unlike the traditional machine learning approaches in learning PDE such as CNN and MLP which require vast parameters for model precision, Neural-PDE shares parameters across all time steps, thus considerably reduces the computational complexity and leads to a fast learning algorithm.
In this paper, we focus on semantically multi-modal image synthesis (SMIS) task, namely, generating multi-modal images at the semantic level. Previous work seeks to use multiple class-specific generators, constraining its usage in datasets with a sma
ll number of classes. We instead propose a novel Group Decreasing Network (GroupDNet) that leverages group convolutions in the generator and progressively decreases the group numbers of the convolutions in the decoder. Consequently, GroupDNet is armed with much more controllability on translating semantic labels to natural images and has plausible high-quality yields for datasets with many classes. Experiments on several challenging datasets demonstrate the superiority of GroupDNet on performing the SMIS task. We also show that GroupDNet is capable of performing a wide range of interesting synthesis applications. Codes and models are available at: https://github.com/Seanseattle/SMIS.
When a blood vessel ruptures or gets inflamed, the human body responds by rapidly forming a clot to restrict the loss of blood. Platelets aggregation at the injury site of the blood vessel occurring via platelet-platelet adhesion, tethering and rolli
ng on the injured endothelium is a critical initial step in blood clot formation. A novel three-dimensional multiscale model is introduced and used in this paper to simulate receptor-mediated adhesion of deformable platelets at the site of vascular injury under different shear rates of blood flow. The novelty of the model is based on a new approach of coupling submodels at three biological scales crucial for the early clot formation: novel hybrid cell membrane submodel to represent physiological elastic properties of a platelet, stochastic receptor-ligand binding submodel to describe cell adhesion kinetics and Lattice Boltzmann submodel for simulating blood flow. The model implementation on the GPUs cluster significantly improved simulation performance. Predictive model simulations revealed that platelet deformation, interactions between platelets in the vicinity of the vessel wall as well as the number of functional GPIb{alpha} platelet receptors played significant roles in the platelet adhesion to the injury site. Variation of the number of functional GPIb{alpha} platelet receptors as well as changes of platelet stiffness can represent effects of specific drugs reducing or enhancing platelet activity. Therefore, predictive simulations can improve the search for new drug targets and help to make treatment of thrombosis patient specific.
In this paper, we introduce a high-order accurate constrained transport type finite volume method to solve ideal magnetohydrodynamic equations on two-dimensional triangular meshes. A new divergence-free WENO-based reconstruction method is developed t
o maintain exactly divergence-free evolution of the numerical magnetic field. A new weighted flux interpolation approach is also developed to compute the z-component of the electric field at vertices of grid cells. We also present numerical examples to demonstrate the accuracy and robustness of the proposed scheme.
