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When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…

The space nonlocal Allen-Cahn equation is a famous example of fractional reaction-diffusion equations. It is also an extension of the classical Allen-Cahn equation, which is widely used in physics to describe the phenomenon of two-phase…

Bayesian filtering is a key tool in many problems that involve the online processing of data, including data assimilation, optimal control, nonlinear tracking and others. Unfortunately, the implementation of filters for nonlinear, possibly…

Implicit models, which allow for the generation of samples but not for point-wise evaluation of probabilities, are omnipresent in real-world problems tackled by machine learning and a hot topic of current research. Some examples include…

Convergence failure and slow convergence rates are among the biggest challenges with solving the system of non-linear equations numerically. Although mitigated, such issues still linger when using strictly small time steps and…

In the past few decades, the development of fluorescent technologies and microscopic techniques has greatly improved scientists' ability to observe real-time single-cell activities. In this paper, we consider the filtering problem associate…

Although the two-layer quasi-geostrophic equations (2QGE) are a simplified model for the dynamics of a stratified, wind-driven ocean, their numerical simulation is still plagued by the need for high resolution to capture the full spectrum…

Twisted particle filters are a class of sequential Monte Carlo methods recently introduced by Whiteley and Lee to improve the efficiency of marginal likelihood estimation in state-space models. The purpose of this article is to extend the…

The explicit filtering method for large eddy simulation (LES,) which comprises integration of the governing equations without any added terms for sub-grid-scale modeling, and the application of a low-pass filter to transported fields, is…

The problem of the optimal allocation (in the expected mean square error sense) of a measurement budget for particle filtering is addressed. We propose three different optimal intermittent filters, whose optimality criteria depend on the…

In this article, we propose a new filtering algorithm based in the Koopman operator, showing that a nonlinear filtering problem can be seen as an equivalent problem where the dynamics is infinite dimensional, but linear. Using Extended…

We present novel model reduction methods for rapid solution of parametrized nonlinear partial differential equations (PDEs) in real-time or many-query contexts. Our approach combines reduced basis (RB) space for rapidly convergent…

The (Non-Preemptive) Throughput Maximization problem is a natural and fundamental scheduling problem. We are given $n$ jobs, where each job $j$ is characterized by a processing time and a time window, contained in a global interval $[0,T)$,…

An algorithm for unconstrained non-convex optimization is described, which does not evaluate the objective function and in which minimization is carried out, at each iteration, within a randomly selected subspace. It is shown that this…

We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…

This paper considers flow problems in multiscale heterogeneous porous media. The multiscale nature of the modeled process significantly complicates numerical simulations due to the need to compute huge and ill-conditioned sparse matrices,…

Iso-surface extraction from an implicit field is a fundamental process in various applications of computer vision and graphics. When dealing with geometric shapes with complicated geometric details, many existing algorithms suffer from high…

Particle filtering algorithms have enabled practical solutions to problems in autonomous robotics (self-driving cars, UAVs, warehouse robots), target tracking, and econometrics, with further applications in speech processing and medicine…

This article presents a constrained policy optimization approach for the optimal control of systems under nonstationary uncertainties. We introduce an assumption that we call Markov embeddability that allows us to cast the stochastic…

Particle filtering is a powerful tool for target tracking. When the budget for observations is restricted, it is necessary to reduce the measurements to a limited amount of samples carefully selected. A discrete stochastic nonlinear…