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Volume 30
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Math. Comput. Appl., Volume 30, Issue 3 (June 2025) – 2 articles

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18 pages, 4321 KiB  
Article
Integrating Equation Coding with Residual Networks for Efficient ODE Approximation in Biological Research
by Ziyue Yi
Math. Comput. Appl. 2025, 30(3), 47; https://doi.org/10.3390/mca30030047 - 27 Apr 2025
Viewed by 113
Abstract
Biological research traditionally relies on experimental methods, which can be inefficient and hinder knowledge transfer due to redundant trial-and-error processes and difficulties in standardizing results. The complexity of biological systems, combined with large volumes of data, necessitates precise mathematical models like ordinary differential [...] Read more.
Biological research traditionally relies on experimental methods, which can be inefficient and hinder knowledge transfer due to redundant trial-and-error processes and difficulties in standardizing results. The complexity of biological systems, combined with large volumes of data, necessitates precise mathematical models like ordinary differential equations (ODEs) to describe interactions within these systems. However, the practical use of ODE-based models is limited by the need for curated data, making them less accessible for routine research. To overcome these challenges, we introduce LazyNet, a novel machine learning model that integrates logarithmic and exponential functions within a Residual Network (ResNet) to approximate ODEs. LazyNet reduces the complexity of mathematical operations, enabling faster model training with fewer data and lower computational costs. We evaluate LazyNet across several biological applications, including HIV dynamics, gene regulatory networks, and mass spectrometry analysis of small molecules. Our findings show that LazyNet effectively predicts complex biological phenomena, accelerating model development while reducing the need for extensive experimental data. This approach offers a promising advancement in computational biology, enhancing the efficiency and accuracy of biological research. Full article
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16 pages, 2341 KiB  
Article
TAE Predict: An Ensemble Methodology for Multivariate Time Series Forecasting of Climate Variables in the Context of Climate Change
by Juan Frausto Solís, Erick Estrada-Patiño, Mirna Ponce Flores, Juan Paulo Sánchez-Hernández, Guadalupe Castilla-Valdez and Javier González-Barbosa
Math. Comput. Appl. 2025, 30(3), 46; https://doi.org/10.3390/mca30030046 - 25 Apr 2025
Viewed by 96
Abstract
Climate change presents significant challenges due to the increasing frequency and intensity of extreme weather events. Mexico, with its diverse climate and geographic position, is particularly vulnerable, underscoring the need for robust strategies to predict atmospheric variables. This work presents TAE Predict (Time [...] Read more.
Climate change presents significant challenges due to the increasing frequency and intensity of extreme weather events. Mexico, with its diverse climate and geographic position, is particularly vulnerable, underscoring the need for robust strategies to predict atmospheric variables. This work presents TAE Predict (Time series Analysis and Ensemble-based Prediction with relevant feature selection) based on relevant feature selection and ensemble models of machine learning. Dimensionality in multivariate time series is reduced through Principal Component Analysis, ensuring interpretability and efficiency. Additionally, data remediation techniques improve data set quality. The ensemble combines Long Short-Term Memory neural networks, Random Forest regression, and Support Vector Machines, optimizing their contributions using heuristic algorithms such as Particle Swarm Optimization. Experimental results from meteorological time series in key Mexican cities demonstrate that the proposed strategy outperforms individual models in accuracy and robustness. This methodology provides a replicable framework for climate variable forecasting, delivering analytical tools that support decision-making in critical sectors, such as agriculture and water resource management. The findings highlight the potential of integrating modern techniques to address complex, high-dimensional problems. By combining advanced prediction models and feature selection strategies, this study advances the reliability of climate forecasts and contributes to the development of effective adaptation and mitigation measures in response to climate change challenges. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2024)
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