The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

: This thesis applies neural network feature selection techniques to multivariate time series data to improve prediction of a target time series. Two approaches to feature selection are used. First, a subset enumeration method is used to determine which financial indicators are most useful for aiding in prediction of the S&P 500 futures daily price. The candidate indicators evaluated include RSI, Stochastics and several moving averages. Results indicate that the Stochastics and RSI indicators result in better prediction results than the moving averages. The second approach to feature selection is calculation of individual saliency metrics. A new decision boundary-based individual saliency metric, and a classifier independent saliency metric are developed and tested. Ruck's saliency metric, the decision boundary based saliency metric, and the classifier independent saliency metric are compared for a data set consisting of the RSI and Stochastics indicators as well as delayed closing price values. The decision based metric and the Ruck metric results are similar, but the classifier independent metric agrees with neither of the other metrics. The nine most salient features, determined by the decision boundary based metric, are used to train a neural network and the results are presented and compared to other published results. (AN)

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Nonlinear Time Series Analysis.

An efficient ghost-cell immersed boundary method (GCIBM) for simulating turbulent flows in complex geometries is presented. A boundary condition is enforced through a ghost cell method. The reconstruction procedure allows systematic development of numerical schemes for treating the immersed boundary while preserving the overall second-order accuracy of the base solver. Both Dirichlet and Neumann boundary conditions can be treated. The current ghost cell treatment is both suitable for staggered and non-staggered Cartesian grids. The accuracy of the current method is validated using flow past a circular cylinder and large eddy simulation of turbulent flow over a wavy surface. Numerical results are compared with experimental data and boundary-fitted grid results. The method is further extended to an existing ocean model (MITGCM) to simulate geophysical flow over a three-dimensional bump. The method is easily implemented as evidenced by our use of several existing codes.

A Ghost-Cell Immersed Boundary Method for Flow in Complex Geometry

Immersed boundary methods for simulating fluid-structure interaction

Fluid-structure interaction involving large deformations: 3D simulations and applications to biological systems

The immersed boundary (IB) method originated by Peskin has been popular in modeling and simulating problems involving the interaction of a flexible structure and a viscous incompressible fluid. The Navier-Stokes (N-S) equations in the IB method are usually solved using numerical methods such as FFT and projection methods. Here in our work, the N-S equations are solved by an alternative approach, the lattice Boltzmann method (LBM). Compared to many conventional N-S solvers, the LBM can be easier to implement and more convenient for modeling additional physics in a problem. This alternative approach adds extra versatility to the immersed boundary method. In this paper we discuss the use of a 3D lattice Boltzmann model (D3Q19) within the IB method. We use this hybrid approach to simulate a viscous flow past a flexible sheet tethered at its middle line in a 3D channel and determine a drag scaling law for the sheet. Our main conclusions are: (1) the hybrid method is convergent with first-order accuracy which is consistent with the immersed boundary method in general; (2) the drag of the flexible sheet appears to scale with the inflow speed which is in sharp contrast with the square law for a rigid body in a viscous flow.

An immersed boundary method based on the lattice Boltzmann approach in three dimensions, with application

An immersed boundary method based on discrete stream function formulation for two- and three-dimensional incompressible flows

Subgrid-scale model for large-eddy simulation of isotropic turbulent flows using an artificial neural network

Coronavirus disease 2019 has become a global pandemic infectious respiratory disease with high mortality and infectiousness This paper investigates respiratory droplet transmission, which is critical to understanding, modeling, and controlling epidemics In the present work, we implemented flow visualization, particle image velocimetry, and particle shadow tracking velocimetry to measure the velocity of the airflow and droplets involved in coughing and then constructed a physical model considering the evaporation effect to predict the motion of droplets under different weather conditions The experimental results indicate that the convection velocity of cough airflow presents the relationship t-0 7 with time;hence, the distance from the cougher increases by t0 3 in the range of our measurement domain Substituting these experimental results into the physical model reveals that small droplets (initial diameter D ≤ 100 μm) evaporate to droplet nuclei and that large droplets with D ≥ 500 μm and an initial velocity u0 ≥ 5 m/s travel more than 2 m Winter conditions of low temperature and high relative humidity can cause more droplets to settle to the ground, which may be a possible driver of a second pandemic wave in the autumn and winter seasons © 2020 Author(s)

The motion of respiratory droplets produced by coughing

The velocities measured by particle image velocimetry (PIV) and particle tracking velocimetry (PTV) commonly provide sparse information on flow motions. A dense velocity field with high resolution is indispensable for data visualization and analysis. In the present work, a physics-informed neural network (PINN) is proposed to reconstruct the dense velocity field from sparse experimental data. A PINN is a network-based data assimilation method. Within the PINN, both the velocity and pressure are approximated by minimizing a loss function consisting of the residuals of the data and the Navier–Stokes equations. Therefore, the PINN can not only improve the velocity resolution but also predict the pressure field. The performance of the PINN is investigated using two-dimensional (2D) Taylor's decaying vortices and turbulent channel flow with and without measurement noise. For the case of 2D Taylor's decaying vortices, the activation functions, optimization algorithms, and some parameters of the proposed method are assessed. For the case of turbulent channel flow, the ability of the PINN to reconstruct wall-bounded turbulence is explored. Finally, the PINN is applied to reconstruct dense velocity fields from the experimental tomographic PIV (Tomo-PIV) velocity in the three-dimensional wake flow of a hemisphere. The results indicate that the proposed PINN has great potential for extending the capabilities of PIV/PTV. 

Shizhao Wang

Papers

An immersed boundary method based on the lattice Boltzmann approach in three dimensions, with application

An immersed boundary method based on discrete stream function formulation for two- and three-dimensional incompressible flows

Subgrid-scale model for large-eddy simulation of isotropic turbulent flows using an artificial neural network

The motion of respiratory droplets produced by coughing

Dense velocity reconstruction from particle image velocimetry/particle tracking velocimetry using a physics-informed neural network