A study of early stopping, ensembling, and patchworking for cascade correlation neural networks

The constructive topology of the cascade correlation algorithm makes it a popular choice for many researchers wishing to utilize neural networks. However, for multimodal problems, the mean squared error of the approximation increases significantly as the number of modes increases. The components of this error will comprise both bias and variance and we provide formulae for estimating these values from mean squared errors alone. We achieve a near threefold reduction in the overall error by using early stopping and ensembling. Also described is a new subdivision technique that we call patchworking. Patchworking, when used in combination with early stopping and ensembling, can achieve an order of magnitude improvement in the error. Also presented is an approach for validating the quality of a neural network’s training, without the explicit use of a testing dataset

Improving the performance of cascade correlation neural networks on multimodal functions

Intrinsic qualities of the cascade correlation algorithm make it a popular choice for many researchers wishing to utilize neural networks. Problems arise when the outputs required are highly multimodal over the input domain. The mean squared error of the approximation increases significantly as the number of modes increases. By applying ensembling and early stopping, we show that this error can be reduced by a factor of three. We also present a new technique based on subdivision that we call patchworking. When used in combination with early stopping and ensembling the mean improvement in error is over 10 in some cases

An optimal factor analysis approach to improve the wavelet-based image resolution enhancement techniques

The existing wavelet-based image resolution enhancement techniques have many assumptions, such as limitation of the way to generate low-resolution images and the selection of wavelet functions, which limits their applications in different fields. This paper initially identifies the factors that effectively affect the performance of these techniques and quantitatively evaluates the impact of the existing assumptions. An approach called Optimal Factor Analysis employing the genetic algorithm is then introduced to increase the applicability and fidelity of the existing methods. Moreover, a new Figure of Merit is proposed to assist the selection of parameters and better measure the overall performance. The experimental results show that the proposed approach improves the performance of the selected image resolution enhancement methods and has potential to be extended to other methods

An academic review: applications of data mining techniques in finance industry

With the development of Internet techniques, data volumes are doubling every two years, faster than predicted by Moore’s Law. Big Data Analytics becomes particularly important for enterprise business. Modern computational technologies will provide effective tools to help understand hugely accumulated data and leverage this information to get insights into the finance industry. In order to get actionable insights into the business, data has become most valuable asset of financial organisations, as there are no physical products in finance industry to manufacture. This is where data mining techniques come to their rescue by allowing access to the right information at the right time. These techniques are used by the finance industry in various areas such as fraud detection, intelligent forecasting, credit rating, loan management, customer profiling, money laundering, marketing and prediction of price movements to name a few. This work aims to survey the research on data mining techniques applied to the finance industry from 2010 to 2015.The review finds that Stock prediction and Credit rating have received most attention of researchers, compared to Loan prediction, Money Laundering and Time Series prediction. Due to the dynamics, uncertainty and variety of data, nonlinear mapping techniques have been deeply studied than linear techniques. Also it has been proved that hybrid methods are more accurate in prediction, closely followed by Neural Network technique. This survey could provide a clue of applications of data mining techniques for finance industry, and a summary of methodologies for researchers in this area. Especially, it could provide a good vision of Data Mining Techniques in computational finance for beginners who want to work in the field of computational finance

Optimisation of the surfboard fin shape using computational fluid dynamics and genetic algorithms

During the sport of wave surfing, the fins on a surfboard play a major role in the overall performance of the surfer. This article presents the optimisation of a surfboard fin shape, using coupled genetic algorithms with the FLUENT® solver, aiming at the maximisation of the lift per drag ratio. The design-variable vector includes six components namely the chord length, the depth and the sweep angle of the fin as well as the maximum camber, the maximum camber position and the thickness of the hydrofoil (the four-digit NACA parametrization). The Latin hypercube sampling technique is utilised to explore the design space, resulting in 42 different fin designs. Fin and control volume models are created (using CATIA® V5) and meshed (unstructured using ANSYS® Workbench). Steady-state computations were performed using the FLUENT SST k−ω (shear stress transport k−ω) turbulence model at the velocity of 10 m/s and 10° angle of attack. Using the obtained lift and drag values, a response surface based model was constructed with the aim to maximise the lift-to-drag ratio. The optimisation problem was solved using the genetic algorithm provided by the MATLAB® optimisation toolbox and the response surface based model was iteratively improved. The resultant optimal fin design is compared with the experimental data for the fin demonstrating an increase in lift-to-drag ratio by approximately 62% for the given angle of attack of 10°

Improvement of the computational performance of a parallel unstructured WENO finite volume CFD code for Implicit Large Eddy Simulation

In this paper the assessment and the enhancement of the computational performance of a high-order finite volume CFD code is presented. Weighted Essentially Non-Oscillatory (WENO) schemes are considered to be from the most computationally expensive numerical frameworks, in the context of high-resolution schemes particularly on hybrid unstructured grids. The focus of this study is to assess the computational bottlenecks of the solver for the WENO schemes for Implicit Large Eddy Simulation (ILES) and optimise the performance and efficiency through a series of code modifications e.g. formula rewriting, reduction of number operations, inclusion of linear systems libraries, non-blocking communications amongst others. The code is assessed on five different HPC systems; significant speed-up is achieved ranging from 1.5 to 8.5, with very high-order schemes benefiting the most. Good scalability is also obtained up to 104 number of cores, demonstrating viability and affordability of WENO type schemes for scale resolving simulations

Numerical investigation of an incompressible flow over a backward facing step using a unified fractional step, artificial compressibility and pressure projection (ESAC-PP) method

This study focuses on an incompressible and laminar flow problem behind a backward facing step by employing a recently developed Fractional-Step, Artificial Compressibility and Pressure-Projection (FSAC-PP) method. The FSAC-PP approach unifies Chorin’s fully-explicit Artificial Compressibility (AC) and semiimplicit Fractional-Step Pressure-Projection (FS-PP) methods within the framework of characteristic-based (CB) Godunov-type schemes for solving the incompressible Navier-Stokes equations. The FSAC-PP approach has been originally introduced for low and moderate Reynolds number flows in conjunction with microfluidic and wide range of multiphysics applications. In this work, we demonstrate the applicability of the novel FSAC-PP method to macro-scale separated flows at a moderate Reynolds number. The computational results obtained with the FSAC-PP approach have been compared to the AC method and experimental data to highlight its favorable accuracy and convergence properties for separated flows

Global motion based video super-resolution reconstruction using discrete wavelet transform

Different from the existing super-resolution (SR) reconstruction approaches working under either the frequency-domain or the spatial- domain, this paper proposes an improved video SR approach based on both frequency and spatial-domains to improve the spatial resolution and recover the noiseless high-frequency components of the observed noisy low-resolution video sequences with global motion. An iterative planar motion estimation algorithm followed by a structure-adaptive normalised convolution reconstruction method are applied to produce the estimated low-frequency sub-band. The discrete wavelet transform process is employed to decompose the input low-resolution reference frame into four sub-bands, and then the new edge-directed interpolation method is used to interpolate each of the high-frequency sub-bands. The novelty of this algorithm is the introduction and integration of a nonlinear soft thresholding process to filter the estimated high-frequency sub-bands in order to better preserve the edges and remove potential noise. Another novelty of this algorithm is to provide flexibility with various motion levels, noise levels, wavelet functions, and the number of used low-resolution frames. The performance of the proposed method has been tested on three well-known videos. Both visual and quantitative results demonstrate the high performance and improved flexibility of the proposed technique over the conventional interpolation and the state-of-the-art video SR techniques in the wavelet- domain

A generalised and low-dissipative multi-directional characteristics-based scheme with inclusion of the local Riemann problem investigating incompressible flows without free-surfaces,

In the present study, we develop a generalised Godunov-type multi-directional characteristics-based (MCB) scheme which is applicable to any hyperbolic system for modelling incompressible flows. We further extend the MCB scheme to include the solution of the local Riemann problem which leads to a hybrid mathematical treatment of the system of equations. We employ the proposed scheme to hyperbolic-type incompressible flow solvers and apply it to the Artificial Compressibility (AC) and Fractional-Step, Artificial Compressibility with Pressure Projection (FSAC-PP) method. In this work, we show that the MCB scheme may improve the accuracy and convergence properties over the classical single-directional characteristics-based (SCB) and non-characteristic treatments. The inclusion of a Riemann solver in conjunction with the MCB scheme is capable of reducing the number of iterations up to a factor of 4.7 times compared to a solution when a Riemann solver is not included. Furthermore, we found that both the AC and FSAC-PP method showed similar levels of accuracy while the FSAC-PP method converged up to 5.8 times faster than the AC method for steady state flows. Independent of the characteristics- and Riemann solver-based treatment of all primitive variables, we found that the FSAC-PP method is 7–200 times faster than the AC method per pseudo-time step for unsteady flows. We investigate low- and high-Reynolds number problems for well-established validation benchmark test cases focusing on a flow inside of a lid driven cavity, evolution of the Taylor–Green vortex and forced separated flow over a backward-facing step. In addition to this, comparisons between a central difference scheme with artificial dissipation and a low-dissipative interpolation scheme have been performed. The results show that the latter approach may not provide enough numerical dissipation to develop the flow at high-Reynolds numbers. We found that the inclusion of a Riemann solver is able to overcome this shortcoming. Overall, the proposed generalised Godunov-type MCB scheme provides an accurate numerical treatment with improved convergence properties for hyperbolic-type incompressible flow solvers

Predicting non-linear flow phenomena through different characteristics-based schemes

The present work investigates the bifurcation properties of the Navier–Stokes equations using characteristics-based schemes and Riemann solvers to test their suitability to predict non-linear flow phenomena encountered in aerospace applications. We make use of a single- and multi-directional characteristics-based scheme and Rusanov’s Riemann solver to treat the convective term through a Godunov-type method. We use the Artificial Compressibility (AC) method and a unified Fractional-Step, Artificial Compressibility with Pressure-Projection (FSAC-PP) method for all considered schemes in a channel with a sudden expansion which provides highly non-linear flow features at low Reynolds numbers that produces a non-symmetrical flow field. Using the AC method, our results show that the multi-directional characteristics-based scheme is capable of predicting these phenomena while the single-directional counterpart does not predict the correct flow field. Both schemes and also Riemann solver approaches produce accurate results when the FSAC-PP method is used, showing that the incompressible method plays a dominant role in determining the behaviour of the flow. This also means that it is not just the numerical interpolation scheme which is responsible for the overall accuracy. Furthermore, we show that the FSAC-PP method provides faster convergence and higher level of accuracy, making it a prime candidate for aerospace applications