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In this study, we focus on the modelling of infiltration process in porous media. We use the meshless techniques for efficiently solving the Richards equation which describes unsaturated water flow through soils. The design of approximate…
Coffee rust is one of the main diseases that affect coffee plantations worldwide. This causes an important economic impact in the coffee production industry in countries where coffee is an important part of the economy. A common method for…
An indirect, hybrid Monte Carlo discretization of general relativistic kinetic theory suitable for the development of numerical schemes for radiation transport is presented. The discretization is based on surface flux estimators obtained…
The Metropolis algorithm involves producing a Markov chain to converge to a specified target density $\pi$. In order to improve its efficiency, we can use the Rejection-Free version of the Metropolis algorithm, which avoids the inefficiency…
In this work, we present an extensive computational study on the Ziff-Gulari-Barshad (ZGB) model extended in order to include the spatial diffusion of oxygen atoms and carbon monoxide molecules, both adsorbed on the surface. In our…
Bayesian models have many desirable properties, most notable is their ability to generalize from limited data and to properly estimate the uncertainty in their predictions. However, these benefits come at a steep computational cost as…
In this paper we present a new fast and accurate method for Radial Basis Function (RBF) approximation, including interpolation as a special case, which enables us to effectively find the optimal value of the RBF shape parameter. In…
Energy-Based Models (EBMs) allow for extremely flexible specifications of probability distributions. However, they do not provide a mechanism for obtaining exact samples from these distributions. Monte Carlo techniques can aid us in…
Extractive summarization (ES) aims to generate a concise summary by selecting a subset of sentences from a document while maximizing relevance and minimizing redundancy. Although modern ES systems achieve high accuracy using powerful neural…
Optimal power flow (OPF) is an important problem for power generation and it is in general non-convex. With the employment of renewable energy, it will be desirable if OPF can be solved very efficiently so its solution can be used in real…
Bayesian optimization is a popular method for optimizing expensive black-box functions. Yet it oftentimes struggles in high dimensions where the computation could be prohibitively heavy. To alleviate this problem, we introduce Coordinate…
In this paper, we present the Monte-Carlo Compressive Optimization algorithm, a new method to solve a combinatorial optimization problem that is assumed compressible. The method relies on random queries to the objective function in order to…
In this paper we present a high-order kernel method for numerically solving diffusion and reaction-diffusion partial differential equations (PDEs) on smooth, closed surfaces embedded in $\mathbb{R}^d$. For two-dimensional surfaces embedded…
A new algorithm for Monte Carlo calculation of the double exchange model is studied. The algorithm is commonly applicable to wide classes of strongly correlated electron systems which involve itinerant electrons coupled with…
Quantitative modeling of post-transcriptional regulation process is a challenging problem in systems biology. A mechanical model of the regulatory process needs to be able to describe the available spatio-temporal protein concentration and…
We used a collocation method in refinable spline space to solve a linear dynamical system having fractional derivative in time. The method takes advantage of an explicit derivation rule for the B-spline basis that allows us to efficiently…
Fractional diffusion has become a fundamental tool for the modeling of multiscale and heterogeneous phenomena. However, due to its nonlocal nature, its accurate numerical approximation is delicate. We survey our research program on the…
Scattered data fitting is a frequently encountered problem for reconstructing an unknown function from given scattered data. Radial basis function (RBF) methods have proven to be highly useful to deal with this problem. We describe two…
These lecture notes contain a brief practical introduction to doing density functional theory calculations for crystals using the open source Quantum Espresso software. The level is aimed at graduate students who are studying condensed…
An alternative methodology to evaluate two-electron-repulsion integrals based on numerical approximation is proposed. Computational chemistry has branched into two major fields with methodologies based on quantum mechanics and classical…