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Existing approaches for graph neural networks commonly suffer from the oversmoothing issue, regardless of how neighborhoods are aggregated. Most methods also focus on transductive scenarios for fixed graphs, leading to poor generalization…
Binary embeddings provide efficient and powerful ways to perform operations on large scale data. However binary embedding typically requires long codes in order to preserve the discriminative power of the input space. Thus binary coding…
In the context of simulating precision laser interferometers, we compare via several examples two wavefront decomposition methods: the Mode Expansion Method (MEM) and the Gaussian beam decomposition (GBD) for their precision and…
Exponential random graph models (ERGMs) are a widely used framework for network data, enabling hypothesis testing on the structural mechanisms underlying observed networks. Bayesian ERGMs provide principled uncertainty quantification and…
The mixture model is undoubtedly one of the greatest contributions to clustering. For continuous data, Gaussian models are often used and the Expectation-Maximization (EM) algorithm is particularly suitable for estimating parameters from…
We develop here a semiparametric Gaussian mixture model (SGMM) for unsupervised learning with valuable spatial information taken into consideration. Specifically, we assume for each instance a random location. Then, conditional on this…
The paper is concerned with the development of efficient and accurate solution procedures for the isogeometric boundary element method (BEM) when applied to problems that contain inclusions that have elastic properties different to the…
The idea of using fragment embedding to circumvent the high computational scaling of accurate electronic structure methods while retaining high accuracy has been a long-standing goal for quantum chemists. Traditional fragment embedding…
We present a novel multi-scale embedding scheme that links conventional QM/MM embedding and bootstrap embedding (BE) to allow simulations of large chemical systems on limited quantum devices. We also propose a mixed-basis BE scheme that…
Energy-Based Models (EBMs) present a flexible and appealing way to represent uncertainty. Despite recent advances, training EBMs on high-dimensional data remains a challenging problem as the state-of-the-art approaches are costly, unstable,…
Analysis of the topology of a graph, regular or bipartite one, can be done by clustering for regular ones or co-clustering for bipartite ones. The Stochastic Block Model and the Latent Block Model are two models, which are very similar for…
Conventionally, piecewise polynomials have been used in the boundary elements method (BEM) to approximate unknown boundary values. Since infinitely smooth radial basis functions (RBFs) are more stable and accurate than the polynomials for…
Partial differential equations (PDEs) on surfaces arise in a wide range of applications. The closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is a recent embedding method that has been used to solve a…
We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These arise, for example, in groundwater flow modelling, where a…
A novel boundary element method (BEM) removes the classical dependence on explicit fundamental solutions and extends quasi-optimal BEM discretisations to strongly elliptic operators with variable coefficients. The approach constructs a…
Stochastic and conditional simulation methods have been effective towards producing realistic realizations and simulations of spatial numerical models that share equal probability of occurrence. Application of these methods are valuable…
Bootstrap embedding (BE) is a recently developed electronic structure method that has shown great success at treating electron correlation in molecules. Here, we extend BE to treat surfaces and solids where the wave function is represented…
We propose a generalized multiscale finite element method (GMsFEM) based on clustering algorithm to study the elliptic PDEs with random coefficients in the multi-query setting. Our method consists of offline and online stages. In the…
The efficient simulation of Gaussian random fields with flexible correlation structures is fundamental in spatial statistics, machine learning, and uncertainty quantification. In this work, we revisit the \emph{spectral turning-bands} (STB)…
We present a graph-regularized learning of Gaussian Mixture Models (GMMs) in distributed settings with heterogeneous and limited local data. The method exploits a provided similarity graph to guide parameter sharing among nodes, avoiding…