相关论文: Estimating long term behavior of flows without tra…

This article performs a unified convergence analysis of a variety of numerical methods for a model of the miscible displacement of one incompressible fluid by another through a porous medium. The unified analysis is enabled through the…

In ecological studies of pattern formation, models of the competitive-diffusion type are generally singularly perturbed, and the numerical approximation of such models is challenging. In this paper, we present finite element discretization…

Transformers use the dense self-attention mechanism which gives a lot of flexibility for long-range connectivity. Over multiple layers of a deep transformer, the number of possible connectivity patterns increases exponentially. However,…

We propose and analyze numerical schemes for the gradient flow of $Q$-tensor with the quasi-entropy. The quasi-entropy is a strictly convex, rotationally invariant elementary function, giving a singular potential constraining the…

The majority of available numerical algorithms for interfacial two-phase flows either treat both fluid phases as incompressible (constant density) or treat both phases as compressible (variable density). This presents a limitation for the…

We put forth a new computational notion of entropy, measuring the (in)feasibility of sampling high-entropy strings that are consistent with a given generator. Specifically, the i'th output block of a generator G has accessible entropy at…

This paper considers a Leray regularization model of incompressible, non-isothermal fluid flows which uses nonlinear filtering based on indicator functions, and introduces an efficient numerical method for solving it. The proposed method…

Given a set of graphs from some unknown family, we want to generate new graphs from that family. Recent methods use diffusion on either graph embeddings or the discrete space of nodes and edges. However, simple changes to embeddings (say,…

We tackle the problem of sampling from intractable high-dimensional density functions, a fundamental task that often appears in machine learning and statistics. We extend recent sampling-based approaches that leverage controlled stochastic…

We present a flow-control technique in traffic-light intersections, aiming at regulating queue lengths to given reference setpoints. The technique is based on multivariable integrators with adaptive gains, computed at each control cycle by…

A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time…

Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…

Conventional approaches for simulating steady-state distributions of particles under diffusive and advective transport at high P\'eclet numbers involve solving the diffusion and advection equations in at least two dimensions. Here, we…

Quantum transport simulations often use explicit, yet finite, electronic reservoirs. These should converge to the correct continuum limit, albeit with a trade-off between discretization and computational cost. Here, we study this interplay…

We introduce a method for reconstructing an infinitesimal normalizing flow given only an infinitesimal change to a (possibly unnormalized) probability distribution. This reverses the conventional task of normalizing flows -- rather than…

We propose a new method for generating realistic datasets with distribution shifts using any decoder-based generative model. Our approach systematically creates datasets with varying intensities of distribution shifts, facilitating a…

Analyzing and controlling system entropy is a powerful tool for regulating predictability of control systems. Applications benefiting from such approaches range from reinforcement learning and data security to human-robot collaboration. In…

We investigate irreversible aggregation processes driven by a source of small mass clusters. In the spatially homogeneous situation, a well-mixed system is consists of clusters of various masses whose concentrations evolve according to an…

We introduce a novel generative model for the representation of joint probability distributions of a possibly large number of discrete random variables. The approach uses measure transport by randomized assignment flows on the statistical…

Integer-order differential operators were originally used to describe local and isotropic effects, in both space and time. However, in fields like biology, the modelling of complex phenomena with spatial heterogeneity necessitates more…