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In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding…

Quantum kernel methods are a promising branch of quantum machine learning, yet their effectiveness on diverse, high-dimensional, real-world data remains unverified. Current research has largely been limited to low-dimensional or synthetic…

The material point method (MPM) is a hybrid particle-grid method widely used for simulating large deformation with history-dependent behavior. Standard MPM often relies on a dense background grid, which can be highly inefficient when…

Among the algorithms that are likely to play a major role in future exascale computing, the fast multipole method (FMM) appears as a rising star. Our previous recent work showed scaling of an FMM on GPU clusters, with problem sizes in the…

Several emerging petascale architectures use energy-efficient processors with vectorized computational units and in-order thread processing. On these architectures the sustained performance of streaming numerical kernels, ubiquitous in the…

The main objective of the Multiple Kernel k-Means (MKKM) algorithm is to extract non-linear information and achieve optimal clustering by optimizing base kernel matrices. Current methods enhance information diversity and reduce redundancy…

Clustering is an important tool in data analysis, with K-means being popular for its simplicity and versatility. However, it cannot handle non-linearly separable clusters. Kernel K-means addresses this limitation but requires a large kernel…

Scaling up the sparse matrix-vector multiplication kernel on modern Graphics Processing Units (GPU) has been at the heart of numerous studies in both academia and industry. In this article we present a novel non-parametric, self-tunable,…

Approximating kernel functions with random features (RFs)has been a successful application of random projections for nonparametric estimation. However, performing random projections presents computational challenges for large-scale…

CPU-GPU heterogeneous architectures are now commonly used in a wide variety of computing systems from mobile devices to supercomputers. Maximizing the throughput for multi-programmed workloads on such systems is indispensable as one single…

We propose a fine-grained hypergraph model for sparse matrix-matrix multiplication (SpGEMM), a key computational kernel in scientific computing and data analysis whose performance is often communication bound. This model correctly describes…

Kernel principal component analysis (KPCA) is a well-recognized nonlinear dimensionality reduction method that has been widely used in nonlinear fault detection tasks. As a kernel trick-based method, KPCA inherits two major problems. First,…

Quantum computing can empower machine learning models by enabling kernel machines to leverage quantum kernels for representing similarity measures between data. Quantum kernels are able to capture relationships in the data that are not…

The application of quantum computation to accelerate machine learning algorithms is one of the most promising areas of research in quantum algorithms. In this paper, we explore the power of quantum learning algorithms in solving an…

We propose several approaches for solving differential equations (DEs) with quantum kernel methods. We compose quantum models as weighted sums of kernel functions, where variables are encoded using feature maps and model derivatives are…

Building highly non-linear and non-parametric models is central to several state-of-the-art machine learning systems. Kernel methods form an important class of techniques that induce a reproducing kernel Hilbert space (RKHS) for inferring…

Kernel density estimation (KDE) is one of the most widely used nonparametric density estimation methods. The fact that it is a memory-based method, i.e., it uses the entire training data set for prediction, makes it unsuitable for most…

Quasiperiodic systems are important space-filling ordered structures, without decay and translational invariance. How to solve quasiperiodic systems accurately and efficiently is of great challenge. A useful approach, the projection method…

Kernel methods play an important role in machine learning applications due to their conceptual simplicity and superior performance on numerous machine learning tasks. Expressivity of a machine learning model, referring to the ability of the…

The Material Point Method (MPM) has become a cornerstone of physics-based simulation, widely used in geomechanics and computer graphics for modeling phenomena such as granular flows, viscoelasticity, fracture mechanics, etc. Despite its…