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Branch and bound algorithms have been developed for reliability analysis of coherent systems. They exhibit a set of advantages; in particular, they can find a computationally efficient representation of a system failure or survival event,…

As a counterpoint to classical stochastic particle methods for diffusion, we develop a deterministic particle method for linear and nonlinear diffusion. At first glance, deterministic particle methods are incompatible with diffusive partial…

We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…

In this work we introduce a new class of gradient-free global optimization methods based on a binary interaction dynamics governed by a Boltzmann type equation. In each interaction the particles act taking into account both the best…

Interacting particle methods are increasingly used to sample from complex and high-dimensional distributions. These stochastic particle integration techniques can be interpreted as an universal acceptance-rejection sequential particle…

Machine learning based partial differential equations (PDEs) solvers have received great attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and…

This paper is concerned with the two new boundary-type radial basis function collocation schemes, boundary knot method (BKM) and boundary particle method (BPM). The BKM is developed based on the dual reciprocity theorem, while the BPM…

Randomized benchmarking (RB) protocols are standard tools for characterizing quantum devices. Prior analyses of RB protocols have not provided a complete method for analyzing realistic data, resulting in a variety of ad-hoc methods. The…

This paper revisits the fundamental equations for the solution of the frictionless unilateral normal contact problem between a rough rigid surface and a linear elastic half-plane using the boundary element method (BEM). After recasting the…

We consider the estimation of Dirichlet Process Mixture Models (DPMMs) in distributed environments, where data are distributed across multiple computing nodes. A key advantage of Bayesian nonparametric models such as DPMMs is that they…

In this paper, we focus on the reduced basis methodology in the context of non-linear non-affinely parametrized partial differential equations in which affine decomposition necessary for the reduced basis methodology are not obtained [4,…

Random reshuffling with momentum (RRM) corresponds to the SGD optimizer with momentum option enabled, as found in many machine learning libraries like PyTorch and TensorFlow. Despite its widespread use, the convergence properties of RRM do…

Restricted Boltzmann Machines (RBMs) are powerful tools for modeling complex systems and extracting insights from data, but their training is hindered by the slow mixing of Markov Chain Monte Carlo (MCMC) processes, especially with highly…

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…

Estimation of Distribution Algorithms (EDAs) require flexible probability models that can be efficiently learned and sampled. Restricted Boltzmann Machines (RBMs) are generative neural networks with these desired properties. We integrate an…

Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction such as Proper Orthogonal Decomposition,…

We propose a distributed bundle adjustment (DBA) method using the exact Levenberg-Marquardt (LM) algorithm for super large-scale datasets. Most of the existing methods partition the global map to small ones and conduct bundle adjustment in…

Numerical homogenization for mechanical multiscale modeling by means of the finite element method (FEM) is an elegant way of obtaining structure-property relations, if the behavior of the constituents of the lower scale is well understood.…

Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…

Random Reshuffling (RR), which is a variant of Stochastic Gradient Descent (SGD) employing sampling without replacement, is an immensely popular method for training supervised machine learning models via empirical risk minimization. Due to…