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Partial differential equation (PDE) models are widely used in engineering and natural sciences to describe spatio-temporal processes. The parameters of the considered processes are often unknown and have to be estimated from experimental…
This work deals with uncertainty quantification for a generic input distribution to some resource-intensive simulation, e.g., requiring the solution of a partial differential equation. While efficient numerical methods exist to compute…
The computation of integrals is a fundamental task in the analysis of functional data, which are typically considered as random elements in a space of squared integrable functions. Borrowing ideas from recent advances in the Monte Carlo…
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…
Mathematical models are an important tool for neuroscientists. During the last thirty years many papers have appeared on single neuron description and specifically on stochastic Integrate and Fire models. Analytical results have been proved…
The execution time of programs is a key element in many areas of computer science, mainly those where achieving good performance (e.g., scheduling in cloud computing) or a predictable one (e.g., meeting deadlines in embedded systems) is the…
The paper presents investigations on the implementation and performance of the finite element numerical integration algorithm for first order approximations and three processor architectures, popular in scientific computing, classical CPU,…
Computational psychiatry is a field aimed at developing formal models of information processing in the human brain, and how alterations in this processing can lead to clinical phenomena. Despite significant progress in the development of…
Complex computer codes are often too time expensive to be directly used to perform uncertainty, sensitivity, optimization and robustness analyses. A widely accepted method to circumvent this problem consists in replacing cpu-time expensive…
We consider the monodomain model, a system of a parabolic semilinear reaction-diffusion equation coupled with a nonlinear ordinary differential equation, arising from the (simplified) mathematical description of the electrical activity of…
The paper deals with the developing of the methodological backgrounds for the modeling and simulation of complex dynamical objects. Such backgrounds allow us to perform coordinate transformation and formulate the algorithm of its usage for…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
Modern computer architectures support low-precision arithmetic, which present opportunities for the adoption of mixed-precision algorithms to achieve high computational throughput and reduce energy consumption. As a growing number of…
Model selection in Gaussian processes scales prohibitively with the size of the training dataset, both in time and memory. While many approximations exist, all incur inevitable approximation error. Recent work accounts for this error in the…
Numerical solutions to fractional differential equations can be extremely computationally intensive due to the effect of non-local derivatives in which all previous time points contribute to the current iteration. In finite difference…
Missing data are often dealt with multiple imputation. A crucial part of the multiple imputation process is selecting sensible models to generate plausible values for incomplete data. A method based on posterior predictive checking is…
We compare failure distributions of quantum error correction circuits for stochastic errors and coherent errors. We utilize a fully coherent simulation of a fault tolerant quantum error correcting circuit for a $d=3$ Steane and surface…
Estimation mainly for two classes of popular models, single-index and partially linear single-index models, is studied in this paper. Such models feature nonstationarity. Orthogonal series expansion is used to approximate the unknown…
A probabilistic circuit (PC) succinctly expresses a function that represents a multivariate probability distribution and, given sufficient structural properties of the circuit, supports efficient probabilistic inference. Typically a PC…
This paper considers the computer model calibration problem and provides a general frequentist solution. Under the proposed framework, the data model is semi-parametric with a nonparametric discrepancy function which accounts for any…