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Open AccessArticle
Proposal of a Modified Loss Function with the Gaussian Copula Density Function to Improve LSTM Predictions of PM10 and PM2.5 Concentrations
by
Alejandro Mendoza-Ibarra
Alejandro Mendoza-Ibarra
Marco Antonio Aceves-Fernandez
Marco Antonio Aceves-Fernandez 
,
Juan Manuel Ramos-Arreguín
Juan Manuel Ramos-Arreguín
Dr. Juan Manuel
Ramos-Arreguin received his M.S. degree in electrical engineering, and digital from [...]
Dr. Juan Manuel
Ramos-Arreguin received his M.S. degree in electrical engineering, option
instrumentation and digital systems, from the University of Guanajuato and his
Ph.D. degree in mechatronics science from the Centro de Ingeniería y Desarrollo
Industrial. He was a professor at the Technological University of San Juan del
Río and at the Center for Engineering and Industrial Development. He has held
positions as President of the Academic Body of Electronics at UTSJR until 2009.
Participant with students in the National Minirobotics Competition until 2008. Member
of the Mexican Mechatronics Association. Currently Professor Researcher of the
Faculty of Informatics at the Autonomous University of Querétaro and member of
the National System of Researchers as a Candidate.
Artemio Sotomayor-Olmedo
Artemio Sotomayor-Olmedo
Facultad de ingeniería, Universidad Autónoma de Querétaro, Carr. Chichimequillas S/N, Querétaro 76140, Mexico
*
Author to whom correspondence should be addressed.
Computers 2026, 15(2), 91; https://doi.org/10.3390/computers15020091 (registering DOI)
Submission received: 2 December 2025
/
Revised: 15 January 2026
/
Accepted: 16 January 2026
/
Published: 1 February 2026
Abstract
Air pollution forecasting for Particulate Matter ( and ) is a challenge for human health in order to improve the life quality of humans around the world. This research focuses on evaluating a Long Short-Term Memory (LSTM) neural network model with an improvement in the loss function using the Gaussian Copula Density function to predict and levels in four stations (AJM, CAM, MER and PED) in Mexico City. The model is compared with a plain LSTM neural network model for forecasting 12, 24, 48 and 72 h using error metrics root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE). The results demonstrate a superior performance of the modified loss function model, achieving the lowest error values across multiple stations and forecast horizons.
Share and Cite
MDPI and ACS Style
Mendoza-Ibarra, A.; Aceves-Fernandez, M.A.; Ramos-Arreguín, J.M.; Sotomayor-Olmedo, A.
Proposal of a Modified Loss Function with the Gaussian Copula Density Function to Improve LSTM Predictions of PM10 and PM2.5 Concentrations. Computers 2026, 15, 91.
https://doi.org/10.3390/computers15020091
AMA Style
Mendoza-Ibarra A, Aceves-Fernandez MA, Ramos-Arreguín JM, Sotomayor-Olmedo A.
Proposal of a Modified Loss Function with the Gaussian Copula Density Function to Improve LSTM Predictions of PM10 and PM2.5 Concentrations. Computers. 2026; 15(2):91.
https://doi.org/10.3390/computers15020091
Chicago/Turabian Style
Mendoza-Ibarra, Alejandro, Marco Antonio Aceves-Fernandez, Juan Manuel Ramos-Arreguín, and Artemio Sotomayor-Olmedo.
2026. "Proposal of a Modified Loss Function with the Gaussian Copula Density Function to Improve LSTM Predictions of PM10 and PM2.5 Concentrations" Computers 15, no. 2: 91.
https://doi.org/10.3390/computers15020091
APA Style
Mendoza-Ibarra, A., Aceves-Fernandez, M. A., Ramos-Arreguín, J. M., & Sotomayor-Olmedo, A.
(2026). Proposal of a Modified Loss Function with the Gaussian Copula Density Function to Improve LSTM Predictions of PM10 and PM2.5 Concentrations. Computers, 15(2), 91.
https://doi.org/10.3390/computers15020091
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