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Mathematics
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Computational Methods in Materials Design
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Computational Methods in Materials Design

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (10 April 2024) | Viewed by 751

Special Issue Editors

Dr. Ignacio Peralta

E-Mail Website
Guest Editor
1. Institute of Construction and Building Materials, Technical University of Darmstadt, 64287 Darmstadt, Germany
2. Research Center for Computational Methods, UNL/CONICET, Santa Fe 3000, Argentina
Interests: computational materials design; smart materials; metamaterials; metadevices; numerical methods; finite elements; computational homogenization; optimization; heat transfer; thermal energy storage
Dr. Víctor D. Fachinotti

E-Mail Website
Guest Editor
Research Center for Computational Methods, UNL/CONICET, Santa Fe 3000, Argentina
Interests: computational design of metamaterials; inverse finite element method; computational metallurgy; building energy simulation; nonlinear constrained optimization

Special Issue Information

Dear Colleagues,

The prospect of finding new materials, with unusual yet effective properties, that transcend the properties of natural materials has captivated the interest of the world’s scientific community. One method of obtaining these new, advanced materials involves the rational manipulation of a material’s microstructure, transforming it into a “smart material” with especially favorable properties for specific engineering applications. This Special Issue invites (but not is not limited to) works that propose the application of mathematical models as well as the implementation of computational tools to design materials with extraordinary and/or controlled properties, as well as macroscopically-controlled response devices, targeting specific engineering applications.

Dr. Ignacio Peralta
Dr. Víctor D. Fachinotti
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. Mathematics 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 2600 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

  • computational materials design
  • smart materials
  • metamaterials
  • metadevices
  • mathematical models
  • computational methods
  • optimization techniques

Published Papers (1 paper)

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Research

15 pages, 2104 KiB  
Article
An Improved Reacceleration Optimization Algorithm Based on the Momentum Method for Image Recognition
by Haijing Sun, Ying Cai, Ran Tao, Yichuan Shao, Lei Xing, Can Zhang and Qian Zhao
Mathematics 2024, 12(11), 1759; https://doi.org/10.3390/math12111759 - 5 Jun 2024
Viewed by 397
Abstract
The optimization algorithm plays a crucial role in image recognition by neural networks. However, it is challenging to accelerate the model’s convergence and maintain high precision. As a commonly used stochastic gradient descent optimization algorithm, the momentum method requires many epochs to find [...] Read more.
The optimization algorithm plays a crucial role in image recognition by neural networks. However, it is challenging to accelerate the model’s convergence and maintain high precision. As a commonly used stochastic gradient descent optimization algorithm, the momentum method requires many epochs to find the optimal parameters during model training. The velocity of its gradient descent depends solely on the historical gradients and is not subject to random fluctuations. To address this issue, an optimization algorithm to enhance the gradient descent velocity, i.e., the momentum reacceleration gradient descent (MRGD), is proposed. The algorithm utilizes the point division of the current momentum and the gradient relationship, multiplying it with the gradient. It can adjust the update rate and step size of the parameters based on the gradient descent state, so as to achieve faster convergence and higher precision in training the deep learning model. The effectiveness of this method is further proven by applying the reacceleration mechanism to the Adam optimizer, resulting in the MRGDAdam algorithm. We verify both algorithms using multiple image classification datasets, and the experimental results show that the proposed optimization algorithm enables the model to achieve higher recognition accuracy over a small number of training epochs, as well as speeding up model implementation. This study provides new ideas and expansions for future optimizer research. Full article
(This article belongs to the Special Issue Computational Methods in Materials Design)
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