Related papers: Multilevel spectral coarsening for graph Laplacian…
Subsampling of node sets is useful in contexts such as multilevel methods, computer graphics, and machine learning. On uniform grid-based node sets, the process of subsampling is simple. However, on node sets with high density variation,…
Existing hybrid Level Set / Front Tracking methods have been developed for structured meshes and successfully used for efficient and accurate simulations of complex multiphase flows. This contribution extends the capability of hybrid Level…
In this paper a numerical multiscale method for discrete networks is presented. The method gives an accurate coarse scale representation of the full network by solving sub-network problems. The method is used to solve problems with highly…
A multilevel correction scheme is proposed to solve defective and nodefective of nonsymmetric partial differential operators by the finite element method. The method includes multi correction steps in a sequence of finite element spaces. In…
Reinforcement learning (RL) is a promising method to solve control problems. However, model-free RL algorithms are sample inefficient and require thousands if not millions of samples to learn optimal control policies. A major source of…
We seek to accelerate and increase the size of simulations for fluid-structure interactions (FSI) by using multiple resolutions in the spatial discretization of the equations governing the time evolution of systems displaying two-way…
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…
We propose a multi-dimensional persistent sheaf Laplacian (MPSL) framework on simplicial complexes for image analysis. The proposed method is motivated by the strong sensitivity of commonly used dimensionality reduction techniques, such as…
Bilevel optimization provides a powerful framework for modelling hierarchical decision-making systems. This work presents a sensitivity-based algorithm that addresses the bilevel structure directly by treating the lower-level optimal…
In this work, we present a novel nonlocal nonlinear coarse grid approximation using a machine learning algorithm. We consider unsaturated and two-phase flow problems in heterogeneous and fractured porous media, where mathematical models are…
This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma…
We develop a multi-level restricted Gaussian maximum likelihood method for estimating the covariance function parameters and computing the best unbiased predictor. Our approach produces a new set of multi-level contrasts where the…
Multi-layer perceptrons (MLPs) are a standard tool for learning and function approximation, but they inherently yield outputs that are globally smooth. As a result, they struggle to represent functions that are continuous yet deliberately…
A model hierarchy that is based on the one-dimensional isothermal Euler equations of fluid dynamics is used for the simulation and optimisation of gas flow through a pipeline network. Adaptive refinement strategies have the aim of bringing…
Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…
Multiscale simulations utilizing high-fidelity, microscopic Monte Carlo models to provide the nonlinear response for continuum models can easily become computationally intractable. Surrogate models for the high-fidelity Monte Carlo models…
Semi-supervised learning is highly useful in common scenarios where labeled data is scarce but unlabeled data is abundant. The graph (or nonlocal) Laplacian is a fundamental smoothing operator for solving various learning tasks. For…
In this paper, we develop a space-time upscaling framework that can be used for many challenging porous media applications without scale separation and high contrast. Our main focus is on nonlinear differential equations with multiscale…
Graph coarsening is a widely used dimensionality reduction technique for approaching large-scale graph machine learning problems. Given a large graph, graph coarsening aims to learn a smaller-tractable graph while preserving the properties…
In this paper, we present a generalisation of the Multilevel Monte Carlo (MLMC) method to a setting where the level parameter is a continuous variable. This Continuous Level Monte Carlo (CLMC) estimator provides a natural framework in PDE…