相关论文: Graph MBO as a semi-discrete implicit Euler scheme…

We present algorithms for solving a large class of flow and regression problems on unit weighted graphs to $(1 + 1 / poly(n))$ accuracy in almost-linear time. These problems include $\ell_p$-norm minimizing flow for $p$ large ($p \in…

The recent introduction of Machine Learning techniques, especially Normalizing Flows, for the sampling of lattice gauge theories has shed some hope on improving the sampling efficiency of the traditional Hybrid Monte Carlo (HMC) algorithm.…

Otto's (2001) Wasserstein gradient flow of the exclusive KL divergence functional provides a powerful and mathematically principled perspective for analyzing learning and inference algorithms. In contrast, algorithms for the inclusive KL…

This paper studies finite element approximations of the stochastic Allen-Cahn equation with gradient-type multiplicative noises that are white in time and correlated in space. The sharp interface limit as the parameter $\epsilon \rightarrow…

We present a nearly-linear time algorithm for finding a minimum-cost flow in planar graphs with polynomially bounded integer costs and capacities. The previous fastest algorithm for this problem is based on interior point methods (IPMs) and…

A classical algorithm by Bellman and Ford from the 1950's computes shortest paths in weighted graphs on $n$ vertices and $m$ edges with possibly negative weights in $O(mn)$ time. Indeed, this algorithm is taught regularly in undergraduate…

Computational fluid dynamics (CFD) is a cornerstone of classical scientific computing, and there is growing interest in whether quantum computers can accelerate such simulations. To date, the existing proposals for fault-tolerant quantum…

In this work, we conduct a detailed comparison between two second-order conservative Allen-Cahn (AC) models [\emph{Model A}: Zheng \emph{et al.}, Phys. Rev. E 101, 0433202 (2020) and \emph{Model B}: Mirjalili and Mani, (2023)] for the…

We consider the fine-grained complexity of sparse graph problems that currently have $\tilde{O}(mn)$ time algorithms, where m is the number of edges and n is the number of vertices in the input graph. This class includes several important…

This paper settles the computational complexity of model checking of several extensions of the monadic second order (MSO) logic on two classes of graphs: graphs of bounded treewidth and graphs of bounded neighborhood diversity. A classical…

We propose a learning-augmented framework for accelerating max-flow computation and image segmentation by integrating Graph Neural Networks (GNNs) with the Ford-Fulkerson algorithm. Rather than predicting initial flows, our method learns…

We present an accelerated, or 'look-ahead' version of the Newton-Dinkelbach method, a well-known technique for solving fractional and parametric optimization problems. This acceleration halves the Bregman divergence between the current…

In this paper we establish the convergence of three computational algorithms for interface motion in a multi-phase system, which incorporate bulk effects. The algorithms considered fall under the classification of thresholding schemes, in…

We introduce a novel discretization scheme for Wasserstein gradient flows that involves successively computing Schr\"{o}dinger bridges with the same marginals. This is different from both the forward/geodesic approximation and the…

We initiate the study of graph algorithms in the streaming setting on massive distributed and parallel systems inspired by practical data processing systems. The objective is to design algorithms that can efficiently process evolving graphs…

In this paper we study minimum cut and maximum flow problems on planar graphs, both in static and in dynamic settings. First, we present an algorithm that given an undirected planar graph computes the minimum cut between any two given…

Circle graphs are intersection graphs of chords of a circle. In this paper, we present a new algorithm for the circle graph isomorphism problem running in time $O((n+m)\alpha(n+m))$ where $n$ is the number of vertices, $m$ is the number of…

The multi-scale nature of gaseous flows poses tremendous difficulties for theoretical and numerical analysis. The Boltzmann equation, while possessing a wider applicability than hydrodynamic equations, requires significantly more…

We study the momentum-based minimization of a diffuse perimeter functional on Euclidean spaces and on graphs with applications to semi-supervised classification tasks in machine learning. While the gradient flow in the task at hand is a…

The physical behaviour of a class of mesoscopic models for multiphase flows is analyzed in details near interfaces. In particular, an extended pseudo-potential method is developed, which permits to tune the equation of state and surface…