Symmetry in Numerical Methods
A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".
Deadline for manuscript submissions: 31 October 2026 | Viewed by 74
Special Issue Editors
Interests: machine learning; deep learning; CNN; LSTM; remote sensing data; mathematical modelling
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
Symmetry is a fundamental principle in the physical sciences that, when mirrored in numerical frameworks, transforms computational efficiency and solution fidelity. In many physical and engineering systems, governing equations exhibit inherent spatial, temporal, or rotational invariances. Exploiting these symmetries allows for strategic reduction, which directly translates to a significant decrease in degrees of freedom, lower memory overhead, and accelerated convergence rates. Further, symmetry-preserving numerical methods, such as equivariant discretizations and structure-preserving integrators, ensure that the discrete model respects the underlying conservation laws of the original continuous system. By maintaining these invariants, solvers can avoid unphysical artifacts and numerical dissipation that often plague "brute-force" approaches. This is especially vital in multi-scale modeling and high-fidelity simulations where the preservation of global properties is as crucial as local accuracy. Ultimately, the systematic integration of symmetry represents a transition from high-cost exhaustive computation to a mathematically rigorous approach that maximizes the utility of modern hardware.
Research topics that land within the scope of this Special Issue include, but are not limited to, the following:
Numerical methods in ODEs and PDEs;
Numerical solutions to Fractional differential equations;
Multi-scale modeling;
Symmetry in discretization;
Numerical efficiency;
Computational fluid dynamics;
Numerical methods in quantum mechanics;
Machine/deep learning, artificial intelligence, neural networks;
Time series forecasting.
We thus call on researchers to contribute to this new Special Issue, with the title “Symmetry in Numerical Methods”, via the MDPI submission system. We look forward to receiving your contributions of reviews and original research articles that help advance this field. The published papers in this Special Issue of Symmetry could provide crucial examples and new possible research directions.
Dr. Dušan Nikezić
Dr. Nikola Mirkov
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-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry 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 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
- numerical methods in ODEs and PDEs
- numerical solutions to fractional differential equations
- multi-scale modeling
- symmetry in discretization
- numerical efficiency
- computational fluid dynamics
- numerical methods in quantum mechanics
- machine/deep learning
- artificial intelligence
- neural networks
- time series forecasting
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