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We propose a kernel compression method for solving Distributed-Order (DO) Fractional Partial Differential Equations (DOFPDEs) at the cost of solving corresponding local-in-time PDEs. The key concepts are (1) discretization of the integral…
Orbital-free density functional theory as an extension of traditional Thomas-Fermi theory has attracted a lot of interest in the past decade because of developments in both more accurate kinetic energy functionals and highly efficient…
The work in this paper is four-fold. Firstly, we introduce an alternative approach to solve fractional ordinary differential equations as an expected value of a random time process. Using the latter, we present an interesting numerical…
We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation…
Multifidelity Monte Carlo methods often rely on a preprocessing phase consisting of standard Monte Carlo sampling to estimate correlation coefficients between models of different fidelity to determine the weights and number of samples for…
We design and analyse the performance of a multilevel ensemble Kalman filter method (MLEnKF) for filtering settings where the underlying state-space model is an infinite-dimensional spatio-temporal process. We consider underlying models…
We study linear rough partial differential equations in the setting of [Friz and Hairer, Springer, 2014, Chapter 12]. More precisely, we consider a linear parabolic partial differential equation driven by a deterministic rough path…
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered datasets in d-dimensional space. It is non-separable approximation, as it is…
The division operation is important for many areas of data processing. Especially considering today's demand for hardware accelerators for machine learning algorithms, there is a high demand for an efficient calculation of the division…
A new method to estimate the Pareto Front (PF) in bi-objective optimization problems is presented. Assuming a continuous PF, the approach, named ROBBO (RObust and Balanced Bi-objective Optimization), needs to sample at most a finite,…
The massive integration of distributed energy resources changes the operational demands of the electric power distribution system, motivating optimization-based approaches. The added computational complexities of the resulting optimal power…
We address the calculation of dynamical correlation functions for many fermion systems at zero temperature, using the auxiliary-field quantum Monte Carlo method. The two-dimensional Hubbard hamiltonian is used as a model system. Although…
When solving stochastic partial differential equations (SPDEs) driven by additive spatial white noise, the efficient sampling of white noise realizations can be challenging. Here, we present a new sampling technique that can be used to…
We present a novel Kalman filter for spatiotemporal systems called the numerical Gaussian process Kalman filter (GPKF). Numerical Gaussian processes have recently been introduced as a physics informed machine learning method for simulating…
Herein, we propose a spatio-temporal extension of RBFNN for nonlinear system identification problem. The proposed algorithm employs the concept of time-space orthogonality and separately models the dynamics and nonlinear complexities of the…
Linear scaling quantum chemical methods for Density Functional Theory are extended to the condensed phase at the $\Gamma$-point. For the two-electron Coulomb matrix, this is achieved with a tree-code algorithm for fast Coulomb summation [J.…
We present a Bayesian data fusion method to approximate a posterior distribution from an ensemble of particle estimates that only have access to subsets of the data. Our approach relies on approximate probabilistic inference of model…
It is well known that using high-order numerical algorithms to solve fractional differential equations leads to almost the same computational cost with low-order ones but the accuracy (or convergence order) is greatly improved, due to the…
We are concerned with the numerical resolution of backward stochastic differential equations. We propose a new numerical scheme based on iterative regressions on function bases, which coefficients are evaluated using Monte Carlo…
A simple yet effective numerical method using orthogonal hybrid functions consisting of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal triangular functions is proposed to solve numerically fractional…