Scientific Computation, Machine Learning and Their Applications in Science and Engineering

Dear Colleagues,

With the swift advancement of artificial intelligence, machine learning, armed with its robust data processing and pattern recognition capabilities, has seamlessly integrated into traditional scientific computation and engineering application domains. From revolutionizing the efficiency of differential equation numerical solutions to achieving technological breakthroughs in natural language processing and computer vision, and further to resolving intricate challenges in disciplines such as engineering and bio-information, the application scope of machine learning continues to broaden, infusing fresh vitality into numerous traditional fields.

To spotlight state-of-the-art accomplishments in the fusion of machine learning and traditional scientific computation, particularly in numerical solving partial differential equations and engineering practices, and to foster in-depth interdisciplinary exchanges and innovative progress, we are launching this Special Issue. This edition is committed to establishing a premier academic exchange platform to disseminate the latest theoretical research, technological advancements and practical applications of research findings in this realm.

We cordially invite experts, scholars, researchers and engineering professionals from both domestic and international circles to actively contribute their papers. The submissions should closely revolve around the theme of integrating machine learning with scientific computing, encompassing both pioneering theoretical explorations and groundbreaking technological achievements in practical applications. Specifically, the following areas are of particular interest:

1. Model and Algorithm Innovation: Develop novel machine-learning models tailored to the demands of solving partial differential equations and design efficient and robust algorithm frameworks. This includes refining integration strategies between finite element methods, finite difference methods and machine learning, as well as exploring optimized applications of supervised, unsupervised and semi-supervised learning in scientific computing.

2. Deep Learning and Neural Network Applications: Delve into the vast potential of deep learning and neural networks in numerical solutions of partial differential equations and engineering system simulations, overcoming the limitations of conventional computational approaches.

3. Engineering Practices in Different Domains: Promote the innovative application of the aforementioned methodologies across diverse sectors such as mineral extraction, biomedicine, biomedical engineering, energy and environmental sciences, artificial intelligence and signal processing. This aims to tackle complex nonlinear engineering difficulties encountered in real-world production and scientific research.

I eagerly anticipate your contributions and hope your manuscript will offer novel insights and methodologies for the integrated development of machine learning and scientific computing.

Prof. Dr. Hongen Jia
Prof. Dr. Ruiping Niu
Dr. Jian Huang
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 250 words) can be sent to the Editorial Office for assessment.

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-anonymized 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.

• numerical solution of partial differential equations
• deep learning
• machine learning
• neural network
• multivariate time series function
• nonlinear engineering problems
• finite element method
• artificial intelligence
• information processing
• finite difference method
• spectral method