Advances in Machine Learning and Mathematical Modelling for Data-Driven Discovery

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 31 August 2026 | Viewed by 1099

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Department of Computer Science, Faculty of Sciences, University of Porto, 4169-007 Porto, Portugal
Interests: data science; machine learning; natural language processing; data visualization
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Special Issue Information

Dear Colleagues,

The rapid expansion of machine learning and data science continues to transform research and practice across multiple scientific domains. This Special Issue, “Advances in Machine Learning and Mathematical Modelling for Data-Driven Discovery”, invites contributions that explore innovative methods, models, and applications that bridge mathematical foundations with real-world data challenges.

We welcome studies addressing predictive and generative modelling, representation learning, and explainable approaches that enhance the reliability, interpretability, and scalability of data-driven systems. Particular emphasis is placed on mathematical and statistical frameworks that strengthen model generalization, support uncertainty quantification, and enable the integration of domain knowledge into learning processes.

Applications in health, biology, social sciences, and engineering are especially encouraged, as they illustrate how mathematical modelling and machine learning jointly contribute to solving complex problems in diagnosis, forecasting, decision support, and scientific discovery. We also welcome contributions on visual analytics and interpretable visualization, which remain central to transforming data into insight and supporting evidence-based reasoning.

The aim of this Special Issue is to highlight recent advances that connect methodological innovation with impactful applications, reinforcing the role of machine learning and mathematical modelling in driving the next generation of data-driven discovery.

Dr. Alvaro Figueira
Guest Editor

Manuscript Submission Information

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Keywords

  • machine learning
  • mathematical modelling
  • predictive modelling
  • explainable artificial intelligence (XAI)
  • uncertainty quantification
  • data visualization
  • interpretability
  • health, social media, engineering and biological data
  • data-driven discovery
  • deep-learning
  • large language models

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Published Papers (1 paper)

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Review

31 pages, 6593 KB  
Review
Trustworthy Machine Learning and Mathematical Modelling for Lithium-Ion Battery State-of-Health Estimation
by Muhammad Sohail, Mohad Tanveer and Heung Soo Kim
Mathematics 2026, 14(11), 1879; https://doi.org/10.3390/math14111879 - 28 May 2026
Viewed by 567
Abstract
Accurate estimation of lithium-ion battery state of health (SOH) is essential for reliable battery management, although SOH cannot be measured directly during normal operation. This review considers machine-learning methods for SOH estimation from a mathematical and trustworthiness-oriented perspective. The literature is organised by [...] Read more.
Accurate estimation of lithium-ion battery state of health (SOH) is essential for reliable battery management, although SOH cannot be measured directly during normal operation. This review considers machine-learning methods for SOH estimation from a mathematical and trustworthiness-oriented perspective. The literature is organised by learning the formulation, including supervised regression, sequence learning, multi-task prediction, and weakly physics-guided methods. Attention is given to data representation, evaluation methods, uncertainty estimation, calibration, robustness under distribution shifts, and physical validity of predictions. The reviewed studies indicate that the feature-based models remain effective in small-data settings, whereas deep sequence models show stronger performance when more informative temporal data and stricter evaluation settings are available. Reported results are strongly affected by split design, preprocessing, and differences between training and test conditions, and may be overstated under same-cell evaluation, leakage, or limited cross-condition testing. The reviewed evidence indicates that reliable SOH estimation requires suitable cross-cell or cross-condition evaluation, uncertainty estimates supported by calibration analysis, robustness under operating variation, clear reporting, and agreement with physical battery behaviour. On this basis, benchmark design principles, reporting recommendations, method-selection guidance, and open research problems are presented. Full article
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