Related papers: An Accurate and Efficient Algorithm for The Time-f…
In this article we consider recursive approximations of the smoothing distribution associated to partially observed stochastic differential equations (SDEs), which are observed discretely in time. Such models appear in a wide variety of…
Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…
Bayesian decision theory advocates the Bayes classifier as the optimal approach for minimizing the risk in machine learning problems. Current deep learning algorithms usually solve for the optimal classifier by \emph{implicitly} estimating…
This paper proposes a new detection algorithm for MIMO communication systems employing high order QAM constellations. The factor graph that corresponds to this problem is very loopy; in fact, it is a complete graph. Hence, a straightforward…
Despite rapid progress in the development of quantum algorithms in quantum computing as well as numerical simulation methods in classical computing for atomic and molecular applications, no systematic and comprehensive electronic structure…
We propose a sequential Monte Carlo (SMC) method to efficiently and accurately compute cut-Bayesian posterior quantities of interest, variations of standard Bayesian approaches constructed primarily to account for model misspecification. We…
In this work, a study of epitaxial growth was carried out by means of wavelets formalism. We showed the existence of a dynamic scaling form in wavelet discriminated linear MBE equation where diffusion and noise are the dominant effects. We…
Solutions to fractional models inherently exhibit non-smooth behavior, which significantly deteriorates the accuracy and therefore efficiency of existing numerical methods. We develop a two-stage data-infused computational framework for…
Caputo-Fabrizio fractional delta derivatives on an arbitrary time scale are presented. When the time scale is chosen to be the set of real numbers, then the Caputo-Fabrizio fractional derivative is recovered. For isolated or partly…
We introduce a discrete scheme for second order fully nonlinear parabolic PDEs with Caputo's time fractional derivatives. We prove the convergence of the scheme in the framework of the theory of viscosity solutions. The discrete scheme can…
We propose a time-adaptive predictor/multi-corrector method to solve hyperbolic partial differential equations, based on the generalized-$\alpha$ scheme that provides user-control on the numerical dissipation and second-order accuracy in…
Time-fractional parabolic equations with a Caputo time derivative are considered. For such equations, we explore and further develop the new methodology of the a-posteriori error estimation and adaptive time stepping proposed in [7]. We…
In this paper, we investigate the numerical approximation of Hamilton-Jacobi equations with the Caputo time-fractional derivative. We introduce an explicit in time discretization of the Caputo derivative and a finite difference scheme for…
This paper introduces a semi-discrete implicit Euler (SDIE) scheme for the Allen-Cahn equation (ACE) with fidelity forcing on graphs. Bertozzi and Flenner (2012) pioneered the use of this differential equation as a method for graph…
Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…
Approximate Bayesian computation (ABC) using a sequential Monte Carlo method provides a comprehensive platform for parameter estimation, model selection and sensitivity analysis in differential equations. However, this method, like other…
In this contribution we derive and analyze a new numerical method for kinetic equations based on a variable transformation of the moment approximation. Classical minimum-entropy moment closures are a class of reduced models for kinetic…
In this work, we explore a time-fractional diffusion equation of order $\alpha \in (0,1)$ with a stochastic diffusivity parameter. We focus on efficient estimation of the expected values (considered as an infinite dimensional integral on…
Fractional derivative relaxation type equations (FREs) including fractional diffusion equation and fractional relaxation equation, have been widely used to describe anomalous phenomena in physics. To utilize the characteristics of…
This paper is concerned with the fractional evolution equation with a discrete distribution of Caputo time-derivatives such that the largest and the smallest orders, $\alpha$ and $\alpha_m$, satisfy the conditions $1<\alpha\le 2$ and…