Related papers: A gradient-augmented level set method with an opti…
Higher-order numerical methods are used to find accurate numerical solutions to hyperbolic partial differential equations and equations of transport type. Limiting is required to either converge to the correct type of solution or to adhere…
A recent novel extension of multi-output Gaussian processes handles heterogeneous outputs assuming that each output has its own likelihood function. It uses a vector-valued Gaussian process prior to jointly model all likelihoods' parameters…
Level proximal subdifferential was introduced by Rockafellar recently for studying proximal mappings of possibly nonconvex functions. In this paper a systematic study of level proximal subdifferential is given. We characterize variational…
Spectral graph contrastive learning often constructs low- and high-frequency views to capture complementary graph signals, but these views are commonly combined by graph-level or node-agnostic fusion rules. We show that graph-level fusion…
Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…
A gradient enhanced ADMM algorithm for optimal transport on general surfaces is proposed in this paper. Based on Benamou and Brenier's dynamical formulation, we combine gradient recovery techniques on surfaces with the ADMM algorithm, not…
To train a well performing neural network for semantic segmentation, it is crucial to have a large dataset with available ground truth for the network to generalize on unseen data. In this paper we present novel point cloud augmentation…
Variational Level Set (LS) has been a widely used method in medical segmentation. However, it is limited when dealing with multi-instance objects in the real world. In addition, its segmentation results are quite sensitive to initial…
Learning and analyzing 3D point clouds with deep networks is challenging due to the sparseness and irregularity of the data. In this paper, we present a data-driven point cloud upsampling technique. The key idea is to learn multi-level…
We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence…
Gradient reconstruction is a key process for the spatial accuracy and robustness of finite volume method, especially in industrial aerodynamic applications in which grid quality affects reconstruction methods significantly. A novel gradient…
This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated and its convergence properties are summarized. Throughout this…
The Gradient Scheme framework provides a unified analysis setting for many different families of numerical methods for diffusion equations. We show in this paper that the Gradient Scheme framework can be adapted to elasticity equations, and…
In this work, we present a new efficient method for convex shape representation, which is regardless of the dimension of the concerned objects, using level-set approaches. Convexity prior is very useful for object completion in computer…
In this paper, we focus on simple bilevel optimization problems, where we minimize a convex smooth objective function over the optimal solution set of another convex smooth constrained optimization problem. We present a novel bilevel…
Thesedays, Convolutional Neural Networks are widely used in semantic segmentation. However, since CNN-based segmentation networks produce low-resolution outputs with rich semantic information, it is inevitable that spatial details (e.g.,…
We have developed a new embedding method for solving scalar hyperbolic conservation laws on surfaces. The approach represents the interface implicitly by a signed distance function following the typical level set method and some embedding…
Despite data augmentation being a de facto technique for boosting the performance of deep neural networks, little attention has been paid to developing augmentation strategies for generative adversarial networks (GANs). To this end, we…
We study level set teleportation, an optimization routine which tries to accelerate gradient descent (GD) by maximizing the gradient norm over a level set of the objective. While teleportation intuitively speeds-up GD via bigger steps,…
We propose a WENO finite difference scheme to approximate anelastic flows, and scalars advected by them, on staggered grids. In contrast to existing WENO schemes on staggered grids, the proposed scheme is designed to be arbitrarily…