This paper is devoted to the construction and analysis of uniformly accurate nested Picard iterative integrators (NPI) for Dirac equation in nonrelativistic limit regime. In this regime, there a dimensionless parameter $\varepsilon\in(0,1]$ inversely proportional speed light admits propagating waves with $O(1)$ wavelength space $O(\varepsilon^2)$ time. To overcome difficulty induced by temporal $\varepsilon$ dependent oscillation, we present several NPI methods which are first-, second-,...

Estimation of model parameters computer simulators, also known as calibration, is an important topic in many engineering applications. In this paper we consider the calibration with help design knowledge. We introduce concept sensible (calibration) variables. Sensible variables are parameters, which sensitive modeling, and whose optimal values differ from values. propose effective method to identify determine appropriate levels for limited physical experimental data. The methodology applied...

In this work, we propose a symmetric exponential-type low- regularity integrator for solving the nonlinear Klein-Gordon equation under rough data. The scheme is explicit in physical space, and it efficient Fourier pseudospectral discretization. Moreover, achieves second-order accuracy time without loss of solution, its time-reversal symmetry ensures good long-time behavior. Error estimates are done both semi- full discretizations. Numerical results confirm theoretical results, comparisons...

A multiscale time integrator Fourier pseudospectral (MTI-FP) method is proposed and rigorously analyzed for the nonlinear Dirac equation (NLDE), which involves a dimensionless parameter ε ∈ (0, 1] inversely proportional to speed of light. The solution NLDE propagates waves with wavelength O ( 2 ) (1) in space, respectively. In nonrelativistic regime, i.e. , 0 < ≪ 1, rapid temporal oscillation causes significantly numerical burdens, making it quite challenging designing analyzing methods...

Kernel ridge regression is an important nonparametric method for estimating smooth functions. We introduce a new set of conditions under which the actual rates convergence kernel estimator both $L_2$ norm and reproducing Hilbert space exceed standard minimax rates. An application this theory leads to understanding Kennedy--O'Hagan approach [J. R. Stat. Soc. Ser. B. Methodol., 63 (2001), pp. 425--464] calibrating model parameters computer simulation. prove that, certain conditions,...

Computer experiments can emulate the physical systems, help computational investigations, and yield analytic solutions. They have been widely employed with many engineering applications (e.g., aerospace, automotive, energy systems). Conventional Bayesian optimization did not incorporate nested structures in computer experiments. This article proposes a novel method for complex multistep or hierarchical characteristics. We prove theoretical properties of outputs given that distribution is...

The variational iteration method was originally proposed to solve non-linear problems of differential equations, this paper shows that it is also a powerful mathematical tool local fractional equations.Two modified Korteweg-de Vries equations are used as examples reveal the simple solution process.

<abstract><p>A Susceptible Infective Recovered (SIR) model is usually unable to mimic the actual epidemiological system exactly. The reasons for this inaccuracy include observation errors and discrepancies due assumptions simplifications made by SIR model. Hence, work proposes calibration prediction methods with a one-time reported number of infected cases. Given that data are assumed be heteroscedastic, we propose two predictors predict modeling discrepancy through Gaussian...

AbstractThe two-layer computer simulators are commonly used to mimic multi-physics phenomena or systems. Usually, the outputs of first-layer simulator (also called inner simulator) partial inputs second-layer outer simulator). How design experiments by considering space-filling properties and simultaneously is a significant challenge that has received scant attention in literature. To address this problem, we propose new sequential optimal Latin hypercube (LHD) using maximin integrating...

Computer simulations are widely used in scientific exploration and engineering designs. However, computer outputs usually do not match the reality perfectly because models built under certain simplifications approximations. When physical observations also available, statistical methods can be applied to estimate discrepancy between output response. In this article, we propose a semi-parametric method for adjustments models. The proposed is proven enjoy nice theoretical properties. We use...

The problem with computer model calibration by tuning the parameters associated models is significant in many engineering and scientific applications. Although several methods have been established to estimate parameters, research focusing on design of remains limited. Therefore, this paper proposes a sequential experiment based D-optimal criterion, which can efficiently tune while improving prediction ability calibrated model. Numerical comparisons simulated real data demonstrate efficiency...

.Computer model calibration is a crucial step in building reliable computer model. In the face of massive physical observations, fast estimation parameters urgently needed. To alleviate computational burden, we design two-step algorithm to estimate by employing subsampling techniques. Compared with current state-of-the-art methods, complexity proposed greatly reduced without sacrificing too much accuracy. We prove consistency and asymptotic normality estimator. The form variance also...

Transportation systems need more accurate predictions to further optimize traffic network design with the development and application of autonomous driving technology. In this article, we focus on highway flow that are often simulated by modified Greenshields model. However, model can not perfectly match true due its underlying simplifications assumptions, implying it is inexact. Specifically, some parameters affect simulation accuracy model, while tuning these improve model’s called...