Related papers: AutoAMG($\theta$): An Auto-tuned AMG Method Based …

Multigrid methods have proven to be an invaluable tool to efficiently solve large sparse linear systems arising in the discretization of partial differential equations (PDEs). Algebraic multigrid methods and in particular adaptive algebraic…

The successes of deep learning, variational inference, and many other fields have been aided by specialized implementations of reverse-mode automatic differentiation (AD) to compute gradients of mega-dimensional objectives. The AD…

Algorithm learning is a core problem in artificial intelligence with significant implications on automation level that can be achieved by machines. Recently deep learning methods are emerging for synthesizing an algorithm from its…

Graph-based accelerators have been widely adopted in symbolic data processing applications such as genomics, cybersecurity, and artificial intelligence. However, these systems often suffer from excessive memory usage and inefficiencies…

Existing fine-tuning methods use a single learning rate over all layers. In this paper, first, we discuss that trends of layer-wise weight variations by fine-tuning using a single learning rate do not match the well-known notion that…

The support vector machine is a flexible optimization-based technique widely used for classification problems. In practice, its training part becomes computationally expensive on large-scale data sets because of such reasons as the…

Graph transformers have gained popularity in various graph-based tasks by addressing challenges faced by traditional Graph Neural Networks. However, the quadratic complexity of self-attention operations and the extensive layering in graph…

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…

Deep learning has recently become one of the most compute/data-intensive methods and is widely used in many research areas and businesses. One of the critical challenges of deep learning is that it has many parameters that can be adjusted,…

Adaptive optimizers, such as Adam, have achieved remarkable success in deep learning. A key component of these optimizers is the so-called preconditioning matrix, providing enhanced gradient information and regulating the step size of each…

Agglomeration-based strategies are important both within adaptive refinement algorithms and to construct scalable multilevel algebraic solvers. In order to automatically perform agglomeration of polygonal grids, we propose the use of…

This paper presents a machine learning-based framework for topology optimization of self-supporting structures, specifically tailored for additive manufacturing (AM). By employing a graph neural network (GNN) that acts as a neural field…

Stochastic gradient methods (SGMs) are the predominant approaches to train deep learning models. The adaptive versions (e.g., Adam and AMSGrad) have been extensively used in practice, partly because they achieve faster convergence than the…

Adversarial Training (AT) with Projected Gradient Descent (PGD) is an effective approach for improving the robustness of the deep neural networks. However, PGD AT has been shown to suffer from two main limitations: i) high computational…

Graph data is ubiquitous in academia and industry, from social networks to bioinformatics. The pervasiveness of graphs today has raised the demand for algorithms that can answer various questions: Which products would a user like to…

The standard goal for an effective algebraic multigrid (AMG) algorithm is to develop relaxation and coarse-grid correction schemes that attenuate complementary error modes. In the nonsymmetric setting, coarse-grid correction $\Pi$ will…

Sparse additive models have attracted much attention in high-dimensional data analysis due to their flexible representation and strong interpretability. However, most existing models are limited to single-level learning under the…

In recent years, the use of machine learning-based surrogate models for computational fluid dynamics (CFD) simulations has emerged as a promising technique for reducing the computational cost associated with engine design optimization.…

Automatic Target Recognition (ATR) algorithms classify a given Synthetic Aperture Radar (SAR) image into one of the known target classes using a set of training images available for each class. Recently, learning methods have shown to…

Automatic machine learning (\AML) is a family of techniques to automate the process of training predictive models, aiming to both improve performance and make machine learning more accessible. While many recent works have focused on aspects…