Related papers: Implicit Active Flux methods for linear advection
In this paper, we propose several novel numerical techniques to deal with nonlinear terms in gradient flows. These step-by-step solving schemes, termed 3S-SAV and 3S-IEQ schemes, are based on recently popular scalar auxiliary variable (SAV)…
We present a novel up-resing technique for generating high-resolution liquids based on scene flow estimation using deep neural networks. Our approach infers and synthesizes small- and large-scale details solely from a low-resolution…
Systems biology relies on mathematical models that often involve complex and intractable likelihood functions, posing challenges for efficient inference and model selection. Generative models, such as normalizing flows, have shown…
Machine learning models are widely regarded as a way forward to tackle multi-query challenges that arise once expensive black-box simulations such as computational fluid dynamics are investigated. However, ensuring the desired level of…
This paper presents a finite volume method for simulating two-phase flows using a level set approach coupled with volume of fluid method capable of simulating sharp fluid interfaces. The efficiency of the method is a result of the fact that…
Many modern datacenter applications involve large-scale computations composed of multiple data flows that need to be completed over a shared set of distributed resources. Such a computation completes when all of its flows complete. A useful…
We study the possibility of using multilevel algorithms for the computation of correlation functions of gradient flow observables. For each point in the correlation function an approximate flow is defined which depends only on links in a…
The computational cost of fluid simulations increases rapidly with grid resolution. This has given a hard limit on the ability of simulations to accurately resolve small scale features of complex flows. Here we use a machine learning…
The anisotropic diffusion equation is imperative in understanding cosmic ray diffusion across the Galaxy, the heliosphere, and its interplay with the ambient magnetic field. This diffusion term contributes to the highly stiff nature of the…
This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…
Data flow analysis and optimization is considered for homogeneous rectangular mesh networks. We propose a flow matrix equation which allows a closed-form characterization of the nature of the minimal time solution, speedup and a simple…
Consider a set of N agents seeking to solve distributively the minimization problem $\inf_{x} \sum_{n = 1}^N f_n(x)$ where the convex functions $f_n$ are local to the agents. The popular Alternating Direction Method of Multipliers has the…
The present paper deals with the problem of improving the efficiency of large scale turbulent flow simulations. The high-fidelity methods for modelling turbulent flows become available for a wider range of applications thanks to the…
We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
A numerical method to efficiently solve for mixing and reaction of scalars in a two-dimensional flow field at large P\'eclet numbers but otherwise arbitrary Damk\"ohler numbers is reported. We consider a strip of one reactant in a pool of…
In this paper we explore acceleration techniques for large scale nonconvex optimization problems with special focuses on deep neural networks. The extrapolation scheme is a classical approach for accelerating stochastic gradient descent for…
The deep-learning-based least squares method has shown successful results in solving high-dimensional non-linear partial differential equations (PDEs). However, this method usually converges slowly. To speed up the convergence of this…
We present an advection-pressure flux-vector splitting method for the one and two- dimensional shallow water equations following the approach first proposed by Toro and V\'azquez for the compressible Euler equations. The resulting…
In this paper we study a system of advection-diffusion equations in a bulk domain coupled to an advection-diffusion equation on an embedded surface. Such systems of coupled partial differential equations arise in, for example, the modeling…