As a general and rigid mathematical tool, wavelet theory has found many applications and is constantly developing. This article reviews the development history of wavelet theory, from the construction method to the discussion of wavelet properties. Then it focuses on the design and expansion of wavelet transform. The main models and algorithms of wavelet transform are discussed. The construction of rational wavelet transform (RWT) is provided by examples emphasizing the advantages of RWT over traditional wavelet transform through a review of the literature. The combination of wavelet theory and neural networks is one of the key points of the review. The review covers the evolution of Wavelet Neural Network (WNN), the system architecture and algorithm implementation. The review of the literature indicates the advantages and a clear trend of fast development in WNN that can be combined with existing neural network algorithms. This article also introduces the categories of wavelet-based applications. The advantages of wavelet analysis are summarized in terms of application scenarios with a comparison of results. Through the review, new research challenges and gaps have been clarified, which will serve as a guide for potential wavelet-based applications and new system designs.

Although Deep Learning (DL) models have been introduced in various fields as effective prediction tools, they often do not care about uncertainty. This can be a barrier to their adoption in real-world applications. The current paper aims to apply and evaluate Monte Carlo (MC) dropout, a computationally efficient approach, to investigate the reliability of several skip connection-based Convolutional Neural Network (CNN) models while keeping their high accuracy. To do so, a high-dimensional regression problem is considered in the context of subterranean fluid flow modeling using 376,250 generated samples. The results demonstrate the effectiveness of MC dropout in terms of reliability with a Standard Deviation (SD) of 0.012–0.174, and of accuracy with a coefficient of determination (R²) of 0.7881–0.9584 and Mean Squared Error (MSE) of 0.0113–0.0508, respectively. The findings of this study may contribute to the distribution of pressure in the development of oil/gas fields.

Accurate prediction of a patient's length of stay in the hospital is important to enable efficient and effective management of hospital beds. This paper studies length-of-stay prediction for pediatric patients with respiratory diseases using three decision tree methods: bagging, Adaboost, and random forest. A data set of 11,206 records retrieved from the hospital information system is used for analysis after preprocessing and transformation into a numerical data type using a computation method and an expansion method. Two testing methods, a bisection test and a periodic test, are designed to assess performance. Bagging shows the best results on the bisection test (0.296 RMSE, 0.831 ${R^{2}}$ , and ${0.723 \pe 1}$ ) on the testing set of the whole data test. The performances of the three methods are similar on the periodic test, whereas Adaboost performs slightly better than the other two methods. This study also investigates the importance of various data fields to the prediction of length of stay. The result of the study indicates that decision tree methods can be used for LOS prediction.