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Mathematical Models and Artificial Intelligence Methods for Digital Twins in Science, Engineering and Medicine

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Computing and Artificial Intelligence".

Deadline for manuscript submissions: 20 September 2025 | Viewed by 1124

Special Issue Editor

Prof. Dr. Francesco Zirilli

E-Mail Website
Guest Editor
Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, 00185 Roma, Italy
Interests: applied mathematics; mathematical modeling in physics and engineering; optimal control; optimization; inverse problems; mathematical finance; numerical methods
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The use of mathematical models in science, engineering and medicine is common. Usually, a model contains unknown parameters that must be determined using data generated from the observation of the phenomenon under investigation. The process of determining the model parameters using the data is called model calibration. The calibrated model can be used for prediction purposes.

In recent years, huge developments in the areas of sensors, telecommunications and computing power have made the emergence of 'digital twin technology' possible. A digital twin can be regarded as an 'enhanced' version of a mathematical model. The main features that characterize a digital twin are as follows:

  1. The dynamical interaction between the physical twin and its digital counterpart. Data taken from the physical twin are fitted and used in the digital twin during the evolution of the phenomenon studied.
  2. The data fitted in the digital twin are relative to the unique physical twin studied. For example, in the medicine, the data are relative to the individual patient under treatment.
  3. The digital twin and, in particular, its prediction capabilities are used in the decision-making process to optimize the outcome of the experiment or of the medical treatment.

The roots of digital twin technology are in aerospace engineering and in robotics. However, today, this technology is a widely applicable set of ideas that can be used in many different situations. Let us mention some of specific contexts where digital twin could be useful:

  1. Science: in the study of climate change.
  2. Engineering: in the governance of complex systems in logistics or in manufacturing. For example, in the manufacturing predictive maintenance of individual physical assets.
  3. Medicine: in precision medicine, where treatment and drugs are designed for the individual patient.

The Special Issue aims to collect contributions that involve mathematical models and/or artificial intelligence methods in the development and use of digital twins. Papers concerned with specific applications are welcome.

Prof. Dr. Francesco Zirilli
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Applied Sciences is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematical model
  • artificial intelligence
  • digital twin
  • sensor
  • numerical method

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Published Papers (3 papers)

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20 pages, 6914 KiB  
Article
Wind Turbine Airfoil Noise Prediction Method Based on Generalized Airfoil Database and Residual Neural Network
by Quan Wang, Haoran Zhang, Xiaodi Wang and Yang Ni
Appl. Sci. 2025, 15(9), 5123; https://doi.org/10.3390/app15095123 - 5 May 2025
Viewed by 336
Abstract
To address the limitations of existing wind turbine airfoil databases, the high computational cost, and low efficiency of noise prediction, this paper proposes a wind turbine airfoil noise prediction method based on generalized airfoil sets and residual neural networks. Firstly, taking a database [...] Read more.
To address the limitations of existing wind turbine airfoil databases, the high computational cost, and low efficiency of noise prediction, this paper proposes a wind turbine airfoil noise prediction method based on generalized airfoil sets and residual neural networks. Firstly, taking a database of 31 commonly used wind turbine airfoils as a reference, a generalized airfoil set with diverse geometric contours was generated. This was achieved by employing airfoil functional integration theory, B-spline curves, and the Class function/Shape function Transformation (CST) method while varying coefficients and control vector parameters. Secondly, the BPM semi-empirical model was used to compute the noise for the generalized airfoil set, which served as the data labels for deep learning. Finally, classical machine learning models were utilized to construct the airfoil noise prediction model. The results demonstrate that the airfoil noise prediction model constructed with the residual neural network (ResNet-18) achieved the highest prediction accuracy, with a mean squared error (MSE) of 0.0282 and a coefficient of determination (R2) of 0.99972. Additionally, the trained model exhibited computational efficiency that was 17.5 times higher than the BPM model. Full article
(This article belongs to the Special Issue Mathematical Models and Artificial Intelligence Methods for Digital Twins in Science, Engineering and Medicine)
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24 pages, 5145 KiB  
Article
Research on Heat Transfer Coefficient Prediction of Printed Circuit Plate Heat Exchanger Based on Deep Learning
by Yi Su, Yongchen Zhao, Jingjin Wu and Ling Zhang
Appl. Sci. 2025, 15(9), 4635; https://doi.org/10.3390/app15094635 - 22 Apr 2025
Viewed by 332
Abstract
The PCHE, as an efficient heat exchanger, plays a crucial role in the storage and regasification of LNG. However, among the existing studies, those that integrate this field with deep learning are scarce. Moreover, research on explainability remains insufficient. To address these gaps, [...] Read more.
The PCHE, as an efficient heat exchanger, plays a crucial role in the storage and regasification of LNG. However, among the existing studies, those that integrate this field with deep learning are scarce. Moreover, research on explainability remains insufficient. To address these gaps, this study first constructs a dataset of heat transfer coefficients (h) through numerical simulations. Pearson correlation analysis is employed to screen out the most influential features. In terms of predictive modeling, the study compares five traditional machine learning models alongside deep learning models such as long short-term memory neural networks (LSTMs), gated recurrent units (GRUs), and Transformer. To further enhance prediction accuracy, three attention mechanisms—self-attention mechanism (SA), squeeze-and-excitation mechanism (SE), and local attention mechanism (LA)—are incorporated into the deep learning models. The experimental results demonstrate that the artificial neural network achieves the best performance among the traditional models, with a prediction accuracy for straight-path h reaching 0.891799 (R2). When comparing deep learning models augmented with attention mechanisms against the baseline models, both LSTM–SE in the linear flow channel and Transformer–LA in the hexagonal flow channel exhibit improved prediction accuracy. Notably, in predicting the heat transfer coefficient of the hexagonal channel, the determination coefficient (R2) of the Transformer–LA model reaches 0.9993, indicating excellent prediction performance. Additionally, this study introduces the SHAP interpretable analysis method to elucidate model predictions, revealing the contributions of different features to model outputs. For instance, in a straight flow channel, the hydraulic diameter (Dh) contributes most significantly to the model output, whereas in a hexagonal flow channel, wall temperature (Tinw) and heat flux (Qw) play more prominent roles. In conclusion, this study offers novel insights and methodologies for PCHE performance prediction by leveraging various machine learning and deep learning models enhanced with attention mechanisms and incorporating explainable analysis methods. These findings not only validate the efficacy of machine learning and deep learning in complex heat exchanger modeling but also provide critical theoretical support for engineering optimization. Full article
(This article belongs to the Special Issue Mathematical Models and Artificial Intelligence Methods for Digital Twins in Science, Engineering and Medicine)
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24 pages, 1017 KiB  
Article
Parametric Estimation and Analysis of Lifetime Models with Competing Risks Under Middle-Censored Data
by Shan Liang and Wenhao Gui
Appl. Sci. 2025, 15(8), 4288; https://doi.org/10.3390/app15084288 - 13 Apr 2025
Viewed by 233
Abstract
Middle-censoring is a general censoring mechanism. In middle-censoring, the exact lifetimes are observed only for a portion of the units and for others, we can only know the random interval within which the failure occurs. In this study, we focus on statistical inference [...] Read more.
Middle-censoring is a general censoring mechanism. In middle-censoring, the exact lifetimes are observed only for a portion of the units and for others, we can only know the random interval within which the failure occurs. In this study, we focus on statistical inference for middle-censored data with competing risks. The latent failure times are assumed to be independent and follow Burr-XII distributions with distinct parameters. To begin with, we derive the maximum likelihood estimators for the unknown parameters, proving their existence and uniqueness. Additionally, asymptotic confidence intervals are constructed using the observed Fisher information matrix. Furthermore, Bayesian estimates under squared loss function and the corresponding highest posterior density intervals are obtained through the Gibbs sampling method. A simulation study is carried out to assess the performance of all proposed estimators. Lastly, an analysis for a practical dataset is provided to demonstrate the inferential processes developed. Full article
(This article belongs to the Special Issue Mathematical Models and Artificial Intelligence Methods for Digital Twins in Science, Engineering and Medicine)
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