A Gaussian Process Method with Uncertainty Quantification for Air Quality Monitoring

The monitoring and forecasting of particulate matter (e.g., PM2.5) and gaseous pollutants (e.g., NO, NO2, and SO2) is of significant importance, as they have adverse impacts on human health. However, model performance can easily degrade due to data noises, environmental and other factors. This paper proposes a general solution to analyse how the noise level of measurements and hyperparameters of a Gaussian process model affect the prediction accuracy and uncertainty, with a comparative case study of atmospheric pollutant concentrations prediction in Sheffield, UK, and Peshawar, Pakistan. The Neumann series is exploited to approximate the matrix inverse involved in the Gaussian process approach. This enables us to derive a theoretical relationship between any independent variable (e.g., measurement noise level, hyperparameters of Gaussian process methods), and the uncertainty and accuracy prediction. In addition, it helps us to discover insights on how these independent variables affect the algorithm evidence lower bound. The theoretical results are verified by applying a Gaussian processes approach and its sparse variants to air quality data forecasting.

Simulation of concentration of an admixture in the multiphase layer with random spherical inclusions

The diffusion of an admixture substance in a multiphase layer with randomly disposed spherical inclusions was investigated. The solution of the initial contact-boundary value problem is obtained in the form of the integral Neumann series. Computer simulation was performed based on the obtained calculation formula. Main regularities of the distributions of the averaged admixture concentration in the layer depending on the values of the diffusion coefficients, density and volume fractions of inclusions were established. The influence of the number of phases of the porous body on the diffusion processes in a multiphase layer with a uniform distribution of spherical inclusions was determined. The dependence of the increase of the averaged concentration function on the characteristic radii of spherical inclusions was analyzed, in particular, it is shown that the behavior of this function does not depend on the ratios of the reduced diffusion coefficients.

An application of the Marchenko internal multiple elimination scheme formulated as a least-squares problem

Seismic images produced by migration of seismic data related to complex geologies, suchas pre-salt environments, are often contaminated by artifacts due to the presence of multipleinternal reflections. These reflections are created when the seismic wave is reflected morethan once in a source-receiver path and can be interpreted as the main coherent noise inseismic data. Several schemes have been developed to predict and subtract internal multiplereflections from measured data, such as the Marchenko multiple elimination (MME) scheme,which eliminates the referred events without requiring a subsurface model or an adaptivesubtraction approach. The MME scheme is data-driven, can remove or attenuate mostof these internal multiples, and was originally based on the Neumann series solution ofMarchenko’s projected equations. However, the Neumann series approximate solution isconditioned to a convergence criterion. In this work, we propose to formulate the MMEas a least-squares problem (LSMME) in such a way that it can provide an alternative thatavoids a convergence condition as required in the Neumann series approach. To demonstratethe LSMME scheme performance, we apply it to 2D numerical examples and compare theresults with those obtained by the conventional MME scheme. Additionally, we evaluatethe successful application of our method through the generation of in-depth seismic images,by applying the reverse-time migration (RTM) algorithm on the original data set and tothose obtained through MME and LSMME schemes. From the RTM results, we show thatthe application of both schemes on seismic data allows the construction of seismic imageswithout artifacts related to internal multiple events.

Low-Complexity Joint Weighted Neumann Series and Gauss-Seidel Soft-Output Detection for Massive MIMO Systems

We introduce a joint weighted Neumann series (WNS) and Gauss-Seidel (GS) approach to implement an approximated linear minimum mean-squared error (LMMSE) detector for uplink massive multiple-input multiple-output (M-MIMO) systems. We first propose to initialize the GS iteration by a WNS method, which produces a closer-to-LMMSE initial solution than the conventional zero vector and diagonal-matrix based scheme. Then the GS algorithm is applied to implement an approximated LMMSE detection iteratively. Furthermore, based on the WNS, we devise a low-complexity approximate log-likelihood ratios (LLRs) computation method whose performance loss is negligible compared with the exact method. Numerical results illustrate that the proposed joint WNS-GS approach outperforms the conventional method and achieves near-LMMSE performance with significantly lower computational complexity.

Born approximation and sequence for hyperbolic equations

The Born approximation and the Born sequence are considered for hyperbolic equations when we perturb their leading parts. The Born approximation is a finite successive approximation such as the finite terms Neumann series for the solution of a hyperbolic equation in terms of the smallness of the perturbation and if the successive approximation is infinitely many times, then we have the Born series. Due to the so called regularity loss for solutions of hyperbolic equations, we need to assume that data such as the inhomogeneous term of the equation, Cauchy datum and boundary datum are C ∞ , and also they satisfy the compatibility condition of any order in order to define the Born series. Otherwise we need to smooth each term of the Born series. The convergence of the Born series and the Born series with smoothing are very natural questions to be asked. Also giving an estimate of approximating the solution for finite terms Born series is also an important question in practice. The aims of this paper are to discuss about these questions. We would like to emphasize that we found a small improvement in the usual energy estimate for solutions of an initial value problem for a hyperbolic equation, which is very useful for our aims. Since the estimate of approximation is only giving the worst estimate for the approximation, we also provide some numerical studies on these questions which are very suggestive for further theoretical studies on the Born approximation for hyperbolic equations.

ANALYTIC DISCRETE-ORDINATES SOLUTION FOR TIME-DEPENDENT TRANSPORT IN FINITE MEDIA

We present an extension of the Analytic Discrete-Ordinates method to time-dependent transport in finite media. The application of this technique to time-dependent transport is primarily accomplished through the use of a Laplace transform. In the case of finite media, a system of equations arises from enforcing boundary conditions. Instead of directly solving this system, we construct a solution in terms of a Neumann series. We then show that terms can be neglected when numerically evaluating the inverse Laplace transform such that the series reduces to a finite sum. With this extension, we use convergence acceleration to generate a high-precision benchmark.