相关论文: A Proximal-Gradient Algorithm for Crystal Surface …

We propose a gradient descent method for solving optimization problems arising in settings of tropical geometry - a variant of algebraic geometry that has attracted growing interest in applications such as computational biology, economics,…

We propose a mini-batching scheme for improving the theoretical complexity and practical performance of semi-stochastic gradient descent applied to the problem of minimizing a strongly convex composite function represented as the sum of an…

We propose and analyse numerical schemes for a system of quasilinear, degenerate evolution equations modelling biofilm growth as well as other processes such as flow through porous media and the spreading of wildfires. The first equation in…

We present an implicit method for solving the diffusion equation for the evolution of the dust fraction in the terminal velocity approximation using dust-as-mixture smoothed particle hydrodynamics (SPH). The numerical scheme involves…

In this paper we establish a rigorous gradient flow structure for one-dimensional Kimura equations with respect to some Wasserstein-Shahshahani optimal transport geometry. This is achieved by first conditioning the underlying stochastic…

We study a Lagrangian numerical scheme for solution of a nonlinear drift diffusion equation of the form $\partial_t u = \partial_x(u \cdot c[\partial_x(h^\prime(u)+v)])$ on an interval. This scheme will consist of a spatio-temporal…

We propose efficient numerical schemes for implementing the natural gradient descent (NGD) for a broad range of metric spaces with applications to PDE-based optimization problems. Our technique represents the natural gradient direction as a…

Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential…

In this paper, we study higher-order-accurate-in-time minimizing movements schemes for Wasserstein gradient flows. We introduce a novel accelerated second-order scheme, leveraging the differential structure of the Wasserstein space in both…

In this paper, we consider a new approach for semi-discretization in time and spatial discretization of a class of semi-linear stochastic partial differential equations (SPDEs) with multiplicative noise. The drift term of the SPDEs is only…

Point discretization of curved surfaces is required in many applications ranging from object rendering to the solution of surface partial differential equations (PDEs). These applications often impose that surfaces are sampled with local…

A numerical method based on smoothed particle hydrodynamics with adaptive spatial resolution (SPH-ASR) was developed for simulating free surface flows. This method can reduce the computational demands while maintaining the numerical…

To acquire the ability to numerically study the rheology of particulate two-phase flows that lack scale separation, we present a general method to average or coarse-grain the equations of motion of a mixture of a continuous fluid of…

The Wasserstein gradient flow structure of the PDE system governing multiphase flows in porous media was recently highlighted in [C. Canc\`es, T. O. Gallou\"et, and L. Monsaingeon, {\it Anal. PDE} 10(8):1845--1876, 2017]. The model can thus…

In this paper, a projected primal-dual gradient flow of augmented Lagrangian is presented to solve convex optimization problems that are not necessarily strictly convex. The optimization variables are restricted by a convex set with…

We propose a projected Wasserstein gradient descent method (pWGD) for high-dimensional Bayesian inference problems. The underlying density function of a particle system of WGD is approximated by kernel density estimation (KDE), which faces…

We study the hybridizable discontinuous Galerkin (HDG) method for the spatial discretization of time fractional diffusion models with Caputo derivative of order $0<\alpha<1$. For each time $t \in [0,T]$, the HDG approximations are taken to…

We present an exponentially convergent semi-implicit meshless algorithm for the solution of Navier-Stokes equations in complex domains. The algorithm discretizes partial derivatives at scattered points using radial basis functions as…

Classical machine learning models such as deep neural networks are usually trained by using Stochastic Gradient Descent-based (SGD) algorithms. The classical SGD can be interpreted as a discretization of the stochastic gradient flow. In…

Sign Gradient Descent (SignGD) is a simple yet robust optimization method, widely used in machine learning for its resilience to gradient noise and compatibility with low-precision computations. While its empirical performance is well…