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Algorithms
Special Issues
AI and Computational Methods in Engineering and Science
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AI and Computational Methods in Engineering and Science

A special issue of Algorithms (ISSN 1999-4893). This special issue belongs to the section "Algorithms for Multidisciplinary Applications".

Deadline for manuscript submissions: 1 July 2025 | Viewed by 2615

Special Issue Editors

Prof. Dr. Dunhui Xiao

E-Mail Website
Guest Editor
School of Mathematical Sciences, Tongji University, Shanghai 200092, China
Interests: AI; machine learning; model reduction; finite element analysis
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Shuai Li

E-Mail Website
Guest Editor
Faculty of Information Technology and Electrical Engineering, University of Oulu, 90570 Oulu, Finland
Interests: robotic manipulation; autonomous manufacturing; multi-robot coordination; intelligent control and optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

AI methods have shown great potential in many fields. Computational simulation or modeling is also a very important area and plays an important role in the environment, ecology, science and engineering. It provides a fantastic tool to help us to understand the world, and it is vital to apply the powerful AI to computational modeling or combine AI and modeling to help us to understand the world better.

This Special Issue welcomes original research articles, reviews, and case studies that explore the diverse applications of AI and computational methods in engineering and science. Contributions may cover a wide range of topics, including, but not limited to, the following:

  • Machine learning and deep learning algorithms for engineering and scientific modeling;
  • Intelligent systems and decision support in engineering and scientific processes;
  • Optimization techniques and evolutionary algorithms for engineering design and problem-solving;
  • Data-driven approaches for predictive modeling, anomaly detection, and fault diagnosis;
  • Simulation and modeling techniques enhanced by AI and computational methods;
  • Big data analytics and data mining in engineering and scientific domains;
  • Integration of AI with Internet of Things (IoT) and cyber–physical systems;
  • AI-enabled robotics and automation in engineering and scientific applications;
  • Computational intelligence in renewable energy systems, environmental sciences, and sustainability;
  • AI-driven image processing, computer vision, and pattern recognition in engineering and science.

This Special Issue will provide a platform for researchers, academics, and industry professionals to share their latest findings, methodologies, and real-world applications in the field of AI and computational methods within engineering and science. We encourage both theoretical and practical contributions that demonstrate the potential and impact of AI-driven approaches to address complex engineering and scientific challenges.

Prof. Dr. Dunhui Xiao
Prof. Dr. Shuai Li
Guest Editors

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. Algorithms is an international peer-reviewed open access monthly 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 1600 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

  • machine learning
  • deep learning
  • AI applications
  • AI applications in environment
  • AI in ecology
  • AI in science and engineering

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue polices can be found here.

Published Papers (3 papers)

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20 pages, 1224 KiB  
Article
A New Generalized Chebyshev Matrix Algorithm for Solving Second-Order and Telegraph Partial Differential Equations
by Waleed Mohamed Abd-Elhameed, Ramy M. Hafez, Anna Napoli and Ahmed Gamal Atta
Algorithms 2025, 18(1), 2; https://doi.org/10.3390/a18010002 - 26 Dec 2024
Viewed by 155
Abstract
This article proposes numerical algorithms for solving second-order and telegraph linear partial differential equations using a matrix approach that employs certain generalized Chebyshev polynomials as basis functions. This approach uses the operational matrix of derivatives of the generalized Chebyshev polynomials and applies the [...] Read more.
This article proposes numerical algorithms for solving second-order and telegraph linear partial differential equations using a matrix approach that employs certain generalized Chebyshev polynomials as basis functions. This approach uses the operational matrix of derivatives of the generalized Chebyshev polynomials and applies the collocation method to convert the equations with their underlying conditions into algebraic systems of equations that can be numerically treated. The convergence and error bounds are examined deeply. Some numerical examples are shown to demonstrate the efficiency and applicability of the proposed algorithms. Full article
(This article belongs to the Special Issue AI and Computational Methods in Engineering and Science)
►▼ Show Figures

Figure 1

Figure 1
<p>Space–time graphs of the approximate solution (<b>left</b>) and the exact solution (<b>right</b>) for Example 1 with <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mi>M</mi> <mo>=</mo> <mn>12</mn> </mrow> </semantics></math>.</p> Full article ">Figure 2
<p>Space–time graphs of the AE functions at <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> for Example 1.</p> Full article ">Figure 3
<p>Comparison of the curves of the analytical solutions and the approximate solutions at <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mspace width="4pt"/> <mn>0.5</mn> <mo>,</mo> <mspace width="4pt"/> <mn>1</mn> </mrow> </semantics></math> (<b>left</b>) and <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <mn>0.0</mn> <mo>,</mo> <mspace width="4pt"/> <mn>0.2</mn> <mo>,</mo> <mspace width="4pt"/> <mn>0.4</mn> </mrow> </semantics></math> (<b>right</b>) for Example 1 with <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mi>M</mi> <mo>=</mo> <mn>12</mn> </mrow> </semantics></math>.</p> Full article ">Figure 4
<p>The AE curves of the <span class="html-italic">z</span>-direction (<b>left</b>) and <math display="inline"><semantics> <mi>τ</mi> </semantics></math>-direction (<b>right</b>) for Example 1 with <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mi>M</mi> <mo>=</mo> <mn>12</mn> </mrow> </semantics></math>.</p> Full article ">Figure 5
<p>Space–time graphs of the approximate solution (<b>left</b>) and its AE function (<b>right</b>) for Example 2 with <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mspace width="4pt"/> <mi mathvariant="script">T</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mi>M</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math>.</p> Full article ">Figure 6
<p>Comparison of the curves of the analytical solutions and the approximate solutions at <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>4</mn> <mo>,</mo> <mspace width="4pt"/> <mn>7</mn> <mo>,</mo> <mspace width="4pt"/> <mn>10</mn> </mrow> </semantics></math> (<b>left</b>) and <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <mn>0.3</mn> <mo>,</mo> <mspace width="4pt"/> <mn>0.6</mn> <mo>,</mo> <mspace width="4pt"/> <mn>0.9</mn> </mrow> </semantics></math> (<b>right</b>) for Example 2 with <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mi>M</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math>.</p> Full article ">Figure 7
<p>Space–time graphs of the approximate solution (<b>left</b>) and its AE function (<b>right</b>) for Example 3 with <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mspace width="4pt"/> <mi mathvariant="script">T</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mi>M</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math>.</p> Full article ">Figure 8
<p>The AE curves of the <span class="html-italic">z</span>-direction (<b>left</b>) and <math display="inline"><semantics> <mi>τ</mi> </semantics></math>-direction (<b>right</b>) for Example 4 with <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mi>M</mi> <mo>=</mo> <mn>16</mn> </mrow> </semantics></math>.</p> Full article ">
16 pages, 7254 KiB  
Article
Partial Discharge Data Augmentation and Pattern Recognition Method Based on DAE-GAN
by Xin Du, Jun Qi, Jiyi Kang, Zezhong Sun, Chunxin Wang and Jun Xie
Algorithms 2024, 17(11), 487; https://doi.org/10.3390/a17110487 - 1 Nov 2024
Viewed by 667
Abstract
Accurate identification of partial discharge (PD) and its types is essential for assessing the operating conditions of electrical equipment. To enhance PD pattern recognition under imbalanced and limited sample conditions, a method based on a Deep Autoencoder-embedded Generative Adversarial Network (DAE-GAN) is proposed. [...] Read more.
Accurate identification of partial discharge (PD) and its types is essential for assessing the operating conditions of electrical equipment. To enhance PD pattern recognition under imbalanced and limited sample conditions, a method based on a Deep Autoencoder-embedded Generative Adversarial Network (DAE-GAN) is proposed. First, the Deep Autoencoder (DAE) is embedded within the Generative Adversarial Network (GAN) to improve the realism of generated samples. Then, complementary PD data samples are introduced during GAN training to address the issue of limited sample size. Lastly, the model’s discriminator is fine-tuned with augmented and balanced training data to enable PD pattern recognition. The DAE-GAN method is used to augment data and recognize patterns in experimental PD signals. The results demonstrate that, under imbalanced and small sample conditions, DAE-GAN generates more authentic PD samples with improved probability distribution fitting compared to other algorithms, leading to varying levels of enhancement in pattern recognition accuracy. Full article
(This article belongs to the Special Issue AI and Computational Methods in Engineering and Science)
►▼ Show Figures

Figure 1

Figure 1
<p>Partial discharge models [<a href="#B21-algorithms-17-00487" class="html-bibr">21</a>].</p> Full article ">Figure 2
<p>Experimental circuit wiring diagram.</p> Full article ">Figure 3
<p>Four different waveforms of PD single pulse [<a href="#B21-algorithms-17-00487" class="html-bibr">21</a>].</p> Full article ">Figure 4
<p>Structure diagrams of DAE and CWGAN-GP.</p> Full article ">Figure 5
<p>Structure diagram of DAE-GAN [<a href="#B21-algorithms-17-00487" class="html-bibr">21</a>].</p> Full article ">Figure 6
<p>Data augmentation and pattern recognition for PD signals based on DAE-GAN.</p> Full article ">Figure 7
<p>Comparison of PD waveforms generated by different models.</p> Full article ">Figure 8
<p>The dimension reduction results of PD samples.</p> Full article ">Figure 9
<p>Probability distribution of dimension reduction samples of local emission signals.</p> Full article ">Figure 10
<p>Diversity comparison of samples generated by models under different conditions.</p> Full article ">
37 pages, 5770 KiB  
Article
A Review on Resource-Constrained Embedded Vision Systems-Based Tiny Machine Learning for Robotic Applications
by Miguel Beltrán-Escobar, Teresa E. Alarcón, Jesse Y. Rumbo-Morales, Sonia López, Gerardo Ortiz-Torres and Felipe D. J. Sorcia-Vázquez
Algorithms 2024, 17(11), 476; https://doi.org/10.3390/a17110476 - 24 Oct 2024
Viewed by 1431
Abstract
The evolution of low-cost embedded systems is growing exponentially; likewise, their use in robotics applications aims to achieve critical task execution by implementing sophisticated control and computer vision algorithms. We review the state-of-the-art strategies available for Tiny Machine Learning (TinyML) implementation to provide [...] Read more.
The evolution of low-cost embedded systems is growing exponentially; likewise, their use in robotics applications aims to achieve critical task execution by implementing sophisticated control and computer vision algorithms. We review the state-of-the-art strategies available for Tiny Machine Learning (TinyML) implementation to provide a complete overview using various existing embedded vision and control systems. Our discussion divides the article into four critical aspects that high-cost and low-cost embedded systems must include to execute real-time control and image processing tasks, applying TinyML techniques: Hardware Architecture, Vision System, Power Consumption, and Embedded Software Platform development environment. The advantages and disadvantages of the reviewed systems are presented. Subsequently, the perspectives of them for the next ten years are present. A basic TinyML implementation for embedded vision application using three low-cost embedded systems, Raspberry Pi Pico, ESP32, and Arduino Nano 33 BLE Sense, is presented for performance analysis. Full article
(This article belongs to the Special Issue AI and Computational Methods in Engineering and Science)
►▼ Show Figures

Figure 1

Figure 1
<p>Block diagram of ESP32-S3 SoC.</p> Full article ">Figure 2
<p>Block diagram of Kendryte K210 SoC.</p> Full article ">Figure 3
<p>Block diagram of ARM Cortex M7 SoC.</p> Full article ">Figure 4
<p>Example of real-time video capture using a webcam and a Raspberry Pi 4.</p> Full article ">Figure 5
<p>Example of real-time video capture using an OV2640 system and an ESP32.</p> Full article ">Figure 6
<p>Content of the Iris dataset.</p> Full article ">Figure 7
<p>DNN architecture tested in Pi Pico, ESP32 and Arduino Nano 33.</p> Full article ">Figure 8
<p>Code snippet in Python loading the Iris dataset and DNN architecture configuration.</p> Full article ">Figure 9
<p>Matrix with input features and matrix with output labels for the DNN.</p> Full article ">Figure 10
<p>Code Snippet with the statement for training and hyperparameters of the DNN.</p> Full article ">Figure 11
<p>Training results. “Loss”: loss function of the training dataset; “val-loss”: validation dataset loss function; “accuracy”: degree of accuracy of the training dataset; “val-accuracy”: degree of accuracy of the validation dataset.</p> Full article ">Figure 12
<p>Training process on the computer.</p> Full article ">Figure 13
<p>Portion of code with the statement of accuracy and the loss function in Python.</p> Full article ">Figure 14
<p>Code snippet with the statement to compress the H5 file and convert it into a tflite file.</p> Full article ">Figure 15
<p>Code snippet in Python used to obtain the accuracy and loss when training and evaluating the model on the computer with the model trained in <span class="html-italic">tflite</span> file.</p> Full article ">Figure 16
<p>Code snippet for obtaining the .cc file in Colab.</p> Full article ">Figure 17
<p>Important hardware parts of selected embedded systems. (<b>a</b>) Arduino Nano 33 BLE Sense Board. (<b>b</b>) Raspberry Pi Pico Board. (<b>c</b>) ESP32 Wroom 32 DevKitc v.1 Board.</p> Full article ">Figure 18
<p>ESP32 Wroom32 module parts.</p> Full article ">Figure 19
<p>TinyML implementation process.</p> Full article ">Figure 20
<p>Code snippet with the headers and libraries required in Arduino IDE for programming the DNN on the ESP32, Pi Pico, and Arduino Nano 33 BLE.</p> Full article ">Figure 21
<p>Code snippet with the main function programmed in Arduino IDE to deploy the DNN within the ESP32, Pi Pico, and Arduino Nano 33 BLE.</p> Full article ">Figure 22
<p>The <span class="html-italic">exercice model.cc</span> file formed by array of hexadecimal data and contained in <span class="html-italic">data.h</span> instance in Arduino IDE.</p> Full article ">Figure 23
<p>Entry dataset for flower type prediction (<b>left</b>) and one-hot tags for the expected prediction (<b>right</b>), in the DNN algorithm deployed on ESP32, Pi Pico, and Nano 33 BLE.</p> Full article ">Figure 24
<p>Results when the flower classification process is deployed within ESP32.</p> Full article ">Figure A1
<p>ESP32 Pinout configuration.</p> Full article ">Figure A2
<p>Raspberry Pi Pico pinout configuration.</p> Full article ">Figure A3
<p>Arduino Nano 33 BLE Sense pinout configuration.</p> Full article ">
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