Abstract

Abstract

A neural network noise prediction model for a turbulent boundary layer noise mechanism has been created using a feed forward multilayer perceptron and a noise spectrum database collected from a family of NACA 0012 areofoils. The results of the neural network model were compared against the Brooks model and it was found that the quality of the prediction was improved was improved over the entire range of the data. The model was also validated against experimental data not utilized the training of the neural, with positive results.

Abstract

Quantitative investment is the process of establishing mathematical models using statistics, information technology, and mathematics to quantify and implement risks, returns, and traditional investment concepts. However, due to the backwardness of computing tools in the past, quantitative investment has not received much recognition. With the improvement of computer science and quantitative analysis theory, traditional fundamental analysis and the use of sampling statistical technology to build advanced mathematical models for investment analysis have failed to meet the requirements of investors. Therefore, the Quantitative investment strategies based on data mining technology are receiving more and more attention. In this paper, we uses MATLAB software to capture big data from financial and economic websites, and then uses neural network training models to predict the trend of stock changes, and finally establishes a suitable quantitative stock selection model. The simulation results show that only by using quantitative stock selection strategies to curb risks and selecting a suitable investment portfolio can achieve the ideal goals in the stock market.

Abstract

Performance metrics (Evaluation metrics or error metrics) are crucial components of regression analysis and machine learning-based prediction models. A performance metric can be defined as a logical and mathematical construct designed to measure how close the predicted outcome is to the actual result. A variety of performance metrics have been described and proposed in the literature. Knowledge about the metrics' properties needs to be systematized to simplify their design and use. In this work, we examine various regression related metrics (14 in total) for continuous variables, including the most widely used ones, such as the (root) mean squared error, the mean absolute error, the Pearson correlation coefficient, and the coefficient of determination, among many others. We provide their mathematical formulations, as well as a discussion on their use, their characteristics, advantages, disadvantages, and limitations, through theoretical analysis and a detailed numerical example. The 10 unitless metrics are further investigated through a numerical analysis with Monte Carlo Simulation based on (i) random guessing and (ii) the addition of random noise with various noise ratios to the predicted values. Some of the metrics show a poor or inconsistent performance, while others exhibit good performance as evaluation measures of the 'goodness of fit'. We highlight the importance of the usage of the right metrics to obtain good predictions in machine learning and regression models in general.

Abstract

Abstract

Abstract

Abstract

Within the framework of linear elastic fracture mechanics, the stress intensity factors (SIFs) are the mostly applied crack-tip characterizing parameters. To obtain the SIFs, approximate formulae are widely used because exact analytical solutions are available only for very simple geometrical and loading configurations [1]. However, even approximate solutions for SIFs are also rather limited to very simple geometrical and loading conditions. In this work, an accurate and efficient SIF prediction model based on Physics-informed neural network (PINN) [4] is developed, where we incorporate the equilibrium equations and constitutive relations into the PINN. In order to capture the singular behavior of the stress and displacement fields around the crack tip, we extend the standard PINN structure by adding two more trainable parameters