Related papers: A gradient-augmented level set method with an opti…
This paper considers a distributed stochastic strongly convex optimization, where agents connected over a network aim to cooperatively minimize the average of all agents' local cost functions. Due to the stochasticity of gradient estimation…
Level-set methods for convex optimization are predicated on the idea that certain problems can be parameterized so that their solutions can be recovered as the limiting process of a root-finding procedure. This idea emerges time and again…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…
This paper proposes a level set-based method for optimizing shell structures with large design changes in shape and topology. Conventional shell optimization methods, whether parametric or nonparametric, often only allow limited design…
Variational empirical Bayes (VEB) methods provide a practically attractive approach to fitting large, sparse, multiple regression models. These methods usually use coordinate ascent to optimize the variational objective function, an…
Many phenomena taking place in the solar photosphere are controlled by plasma motions. Although the line-of-sight component of the velocity can be estimated using the Doppler effect, we do not have direct spectroscopic access to the…
Graph-based models require aggregating information in the graph from neighbourhoods of different sizes. In particular, when the data exhibit varying levels of smoothness on the graph, a multi-scale approach is required to capture the…
In this paper, we develop an adaptive high-order surface finite element method (FEM) incorporating the spectral deferred correction method for chain contour discretization to solve polymeric self-consistent field equations on general curved…
Bayesian experimental design (BED) is to answer the question that how to choose designs that maximize the information gathering. For implicit models, where the likelihood is intractable but sampling is possible, conventional BED methods…
Incremental learning of semantic segmentation has emerged as a promising strategy for visual scene interpretation in the open- world setting. However, it remains challenging to acquire novel classes in an online fashion for the segmentation…
In the current deep learning based recommendation system, the embedding method is generally employed to complete the conversion from the high-dimensional sparse feature vector to the low-dimensional dense feature vector. However, as the…
Gradient descent algorithms have been used in countless applications since the inception of Newton's method. The explosion in the number of applications of neural networks has re-energized efforts in recent years to improve the standard…
Panoptic segmentation combines the advantages of semantic and instance segmentation, which can provide both pixel-level and instance-level environmental perception information for intelligent vehicles. However, it is challenged with…
We consider an arbitrary-Lagrangian-Eulerian evolving surface finite element method for the numerical approximation of advection and diffusion of a conserved scalar quantity on a moving surface. We describe the method, prove optimal order…
Steady state simulations} of magnetized electron fluid equations with strong anisotropic diffusion based on the first-order hyperbolic approach is carried out using cell-centered higher order upwind schemes, linear and weighted essentially…
We present a new method for efficient high-quality image segmentation of objects and scenes. By analogizing classical computer graphics methods for efficient rendering with over- and undersampling challenges faced in pixel labeling tasks,…
We introduce a novel approach to graph-level representation learning, which is to embed an entire graph into a vector space where the embeddings of two graphs preserve their graph-graph proximity. Our approach, UGRAPHEMB, is a general…
A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and…
In this paper, a gradient-free distributed algorithm is introduced to solve a set constrained optimization problem under a directed communication network. Specifically, at each time-step, the agents locally compute a so-called…
In this paper we present a new Eulerian finite element method for the discretization of scalar partial differential equations on evolving surfaces. In this method we use the restriction of standard space-time finite element spaces on a…