scholarly journals Confidence Intervals for Neural Networks and Applications to Modeling Engineering Materials

10.5772/16097 ◽  
2011 ◽  
Author(s):  
Shouling He ◽  
Jiang Li
Keyword(s):  
Neural Networks ◽  
Confidence Intervals ◽  
Engineering Materials

Development of artificial neural networks based confidence intervals and response surfaces for the optimization of coagulation performance

2015 ◽  
Vol 15 (5) ◽  
pp. 1079-1087 ◽  
Author(s):  
Robert H. McArthur ◽  
Robert C. Andrews
Keyword(s):  
Carbon Dioxide ◽  
Neural Networks ◽  
Artificial Neural Networks ◽  
Water Treatment ◽  
Confidence Intervals ◽  
Response Surfaces ◽  
Average Interval ◽  
Squared Error ◽  
Interval Width ◽  
Artificial Neural

Effective coagulation is essential to achieving drinking water treatment objectives when considering surface water. To minimize settled water turbidity, artificial neural networks (ANNs) have been adopted to predict optimum alum and carbon dioxide dosages at the Elgin Area Water Treatment Plant. ANNs were applied to predict both optimum carbon dioxide and alum dosages with correlation (R2) values of 0.68 and 0.90, respectively. ANNs were also used to developed surface response plots to ease optimum selection of dosage. Trained ANNs were used to predict turbidity outcomes for a range of alum and carbon dioxide dosages and these were compared to historical data. Point-wise confidence intervals were obtained based on error and squared error values during the training process. The probability of the true value falling within the predicted interval ranged from 0.25 to 0.81 and the average interval width ranged from 0.15 to 0.62 NTU. Training an ANN using the squared error produced a larger average interval width, but better probability of a true prediction interval.

scholarly journals Global Surface HCHO Distribution Derived from Satellite Observations with Neural Networks Technique

2021 ◽  
Vol 13 (20) ◽  
pp. 4055
Author(s):  
Jian Guan ◽  
Bohan Jin ◽  
Yizhe Ding ◽  
Wen Wang ◽  
Guoxiang Li ◽  
...  
Keyword(s):  
Neural Networks ◽  
Confidence Intervals ◽  
Amazon Basin ◽  
Surface Concentration ◽  
Average Concentration ◽  
Monitoring Networks ◽  
Vertical Column ◽  
Atmospheric Pollutant ◽  
Surface Distribution ◽  
Global Surface

Formaldehyde (HCHO) is one of the most important carcinogenic air contaminants in outdoor air. However, the lack of monitoring of the global surface concentration of HCHO is currently hindering research on outdoor HCHO pollution. Traditional methods are either restricted to small areas or, for research on a global scale, too data-demanding. To alleviate this issue, we adopted neural networks to estimate the 2019 global surface HCHO concentration with confidence intervals, utilizing HCHO vertical column density data from TROPOMI, and in-situ data from HAPs (harmful air pollutants) monitoring networks and the ATom mission. Our results show that the global surface HCHO average concentration is 2.30 μg/m3. Furthermore, in terms of regions, the concentrations in the Amazon Basin, Northern China, South-east Asia, the Bay of Bengal, and Central and Western Africa are among the highest. The results from our study provide the first dataset on global surface HCHO concentration. In addition, the derived confidence intervals of surface HCHO concentration add an extra layer of confidence to our results. As a pioneering work in adopting confidence interval estimation to AI-driven atmospheric pollutant research and the first global HCHO surface distribution dataset, our paper paves the way for rigorous study of global ambient HCHO health risk and economic loss, thus providing a basis for pollution control policies worldwide.

scholarly journals An experiment on the evolution of an ensemble of neural networks for streamflow forecasting

2009 ◽  
Vol 6 (5) ◽  
pp. 6265-6291 ◽  
Author(s):  
M.-A. Boucher ◽  
J.-P. Laliberté ◽  
F. Anctil
Keyword(s):  
Neural Networks ◽  
Confidence Intervals ◽  
Assessment Tools ◽  
Multilayer Perceptrons ◽  
Streamflow Forecasting ◽  
Training Process ◽  
Probability Score ◽  
Continuous Ranked Probability Score ◽  
Ensemble Mean ◽  
The Mean

Abstract. We present an experiment on fifty multilayer perceptrons trained for streamflow forecasting on four watersheds. This type of neural network is common in hydrology and using multiple training repetitions (ensembling) is a popular practice: the information issued by the ensemble is then aggregated and considered to be the final output. Some authors proposed that the ensemble could serve the calculation of confidence intervals around the ensemble mean. In the following, we are interested in the reliability of confidence intervals obtained in such fashion and in tracking the evolution of the ensemble of neural networks during the training process. For each iteration of this process, the mean of the ensemble is computed along with various confidence intervals. The performance of the ensemble mean is evaluated based on the mean absolute error. Since the ensemble of neural networks resemble an ensemble streamflow forecast, we also use ensemble-specific quality assessment tools such as the Continuous Ranked Probability Score to quantify the forecasting performance of the ensemble formed by the neural networks repetitions. We show that while the performance of the single predictor formed by the ensemble mean improves throughout the training process, the reliability of the associated confidence intervals starts to decrease shortly after the initiation of the training process. While there is no moment in the training process where the reliability of the confidence intervals is perfect, we show that it is best after approximately 5 to 10 iterations, depending on the basin. We also show that the Continuous Ranked Probability Score and the logarithmic score do not evolve in the same fashion during the training, due to a particularity of the logarithmic score.

scholarly journals An experiment on the evolution of an ensemble of neural networks for streamflow forecasting

2010 ◽  
Vol 14 (3) ◽  
pp. 603-612 ◽  
Author(s):  
M.-A. Boucher ◽  
J.-P. Laliberté ◽  
F. Anctil
Keyword(s):  
Neural Networks ◽  
Confidence Intervals ◽  
Assessment Tools ◽  
Multilayer Perceptrons ◽  
Streamflow Forecasting ◽  
Training Process ◽  
Probability Score ◽  
Continuous Ranked Probability Score ◽  
Ensemble Mean ◽  
The Mean

Abstract. We present an experiment on fifty multilayer perceptrons trained for streamflow forecasting on three watersheds using bootstrapped input series. This type of neural network is common in hydrology and using multiple training repetitions (ensembling) is a popular practice: the information issued by the ensemble is then aggregated and considered to be the final output. Some authors proposed that the ensemble could serve the calculation of confidence intervals around the ensemble mean. In the following, we are interested in the reliability of confidence intervals obtained in such fashion and in tracking the evolution of the ensemble of neural networks during the training process. For each iteration of this process, the mean of the ensemble is computed along with various confidence intervals. The performance of the ensemble mean is evaluated based on the mean absolute error. Since the ensemble of neural networks resemble an ensemble streamflow forecast, we also use ensemble-specific quality assessment tools such as the Continuous Ranked Probability Score to quantify the forecasting performance of the ensemble formed by the neural networks repetitions. We show that while the performance of the single predictor formed by the ensemble mean improves throughout the training process, the reliability of the associated confidence intervals starts to decrease shortly after the initiation of this process. While there is no moment during the training where the reliability of the confidence intervals is perfect, we show that it is best after approximately 5 to 10 iterations, depending on the basin. We also show that the Continuous Ranked Probability Score and the logarithmic score do not evolve in the same fashion during the training, due to a particularity of the logarithmic score.

Sign in / Sign up

Export Citation Format

Share Document