Related papers: Conservative semi-lagrangian finite difference sch…
We propose a generalized Eulerian-Lagrangian (GEL) discontinuous Galerkin (DG) method. The method is a generalization of the Eulerian-Lagrangian (EL) DG method for transport problems proposed in [arXiv preprint arXiv: 2002.02930 (2020)],…
We develop several efficient numerical schemes which preserve exactly the global constraints for constrained gradient flows. Our schemes are based on the SAV approach combined with the Lagrangian multiplier approach. They are as efficient…
We propose and analyze a modified damped Newton algorithm to solve the semi-discrete optimal transport with storage fees. We prove global linear convergence for a wide range of storage fee functions, the main assumption being that each…
Transport mode detection is a classification problem aiming to design an algorithm that can infer the transport mode of a user given multimodal signals (GPS and/or inertial sensors). It has many applications, such as carbon footprint…
We introduce in this work an efficient numerical method for the simulation of the quantum Liouville-BGK equation, which models the diffusive transport of quantum particles. The corner stone to the model is the BGK collision operator,…
In this paper, we propose a modification of an acoustic-transport operator splitting Lagrange-projection method for simulating compressible flows with gravity. The original method involves two steps that respectively account for acoustic…
We present a subspace method based on neural networks (SNN) for solving the partial differential equation with high accuracy. The basic idea of our method is to use some functions based on neural networks as base functions to span a…
Recently, graph Convolutional Neural Networks (graph CNNs) have been widely used for graph data representation and semi-supervised learning tasks. However, existing graph CNNs generally use a fixed graph which may be not optimal for…
This paper presents a formulation of the reactive dynamic user equilibrium problem in continuum form using a network-level Macroscopic Fundamental Diagram (MFD). Compared to existing continuum models for cities -- all based in Hughes'…
We introduce a Lagrangian nodal discontinuous Galerkin (DG) cell-centered hydrodynamics method for solving multi-dimensional hyperbolic systems. By incorporating an adaptation of Zalesak's flux-corrected transport algorithm, we combine a…
We discretize the Vlasov-Poisson system using conservative semi-Lagrangian (CSL) discontinuous Galerkin (DG) schemes that are asymptotic preserving (AP) in the quasi-neutral limit. The proposed method (CSLDG) relies on two key ingredients:…
In this paper we exploit Semi-Supervised Learning (SSL) to increase the amount of training data to improve the performance of Fine-Grained Visual Categorization (FGVC). This problem has not been investigated in the past in spite of…
We give a new and constructive proof of the existence of global-in-time weak solutions of the 3-dimensional incompressible semi-geostrophic equations (SG) in geostrophic coordinates, for arbitrary initial measures with compact support. This…
We introduce a finite-difference framework for curvature regularization in neural signed distance field (SDF) learning. Existing approaches enforce curvature priors using full Hessian information obtained via second-order automatic…
The Forward-Forward (FF) Algorithm has been recently proposed to alleviate the issues of backpropagation (BP) commonly used to train deep neural networks. However, its current formulation exhibits limitations such as the generation of…
Most existing semi-supervised graph-based clustering methods exploit the supervisory information by either refining the affinity matrix or directly constraining the low-dimensional representations of data points. The affinity matrix…
We develop a class of algorithms, as variants of the stochastically controlled stochastic gradient (SCSG) methods (Lei and Jordan, 2016), for the smooth non-convex finite-sum optimization problem. Assuming the smoothness of each component,…
The selective frequency damping (SFD) method is an alternative to classical Newton's method to obtain unstable steady-state solutions of dynamical systems. However this method has two main limitations: it does not converge for arbitrary…
Recently, graph convolutional network (GCN) has been widely used for semi-supervised classification and deep feature representation on graph-structured data. However, existing GCN generally fails to consider the local invariance constraint…
In this work, we study and extend a class of semi-Lagrangian exponential methods, which combine exponential time integration techniques, suitable for integrating stiff linear terms, with a semi-Lagrangian treatment of nonlinear advection…