Optimizing Systems and Models with Mathematical Formalisms
The Mathematical Formalism Domain Special Interest Group (Math DSIG) applies advanced concepts of mathematics to model-based systems engineering (MBSE) to enhance system performance and the efficient use of models. As modern systems grow more complex, so also do the models for designing and delivering products and services to market. To meet this challenge, advanced mathematical concepts for systems modeling and analysis can simplify this complexity, making it easier to analyze, predict, and optimize system behavior.
By integrating mathematical formalisms into MBSE, organizations can streamline system architecture, improve model accuracy, and accelerate decision-making. The Math DSIG collaborates with OMG working groups to advance the application of mathematical methods in system design.
Our Mission:
Collaboratively work with OMG groups to achieve the following goals:
- Develop mathematical formalisms for OMG model-based frameworks and standards.
- Enable model transformations that simplify system design and analysis through reusable, modular components that can be defined mathematically.
- Establish foundational mathematical principles that support MBSE and can be expressed through OMG modeling standards.
Key Contributions:
The Math DSIG played a pivotal role in the adoption of the Unified Profile for ROSETTA (UPR) standard, which has been applied to wireless charging systems for electric vehicles. Building on this success, the group is now focused on further developing mathematical formalisms to support advanced MBSE methods and applications.
Resources:
- December 2024 Mathsig presentation to the SE DSIG: Interpreting SysMLv2 into the Category of Relations for Architecture, Analysis and Design
- UML Profile for ROSETTA(UPR): Adds capabilities to UML for a comprehensive facility to structure information in support of model based analysis for architecture optimization and system design.
- IEEE Article: Advanced research on how mathematical formalism can be used to define key terms in systems and architecture in a way that is precise yet intuitive, and use these terms to define a model based mathematical process for Architecture Definition in systems engineering.
- Book: A post graduate level textbook on systems engineering that specifies formal transformations between the key models of MBSE using SysML that are suitable for practical engineering.
- Math DSIG Paper: Offers a distilled summary of transformations of graphical models that have been expressed in SysML diagrams, from Use Cases through Sequence Diagrams.
- December 2022 BAE Systems Presentation: Why is mathematical formalism needed in Systems Engineering?
- June 2024 Presentation 1 at Mathsig: Artificial General Intelligence (AGI) realized by Stochastic Fibred Category Theory.
- September 2024 Mathsig Presentation to the AI PTF: A Brief Introduction to Category Theory. A recording of the presentation can be found at, https://www.omg.org/cgi-bin/doc.cgi?ai/2024-09-06
Why Get Involved with Math DSIG?
With expertise spanning advanced research and commercial system applications, the Math DSIG helps organizations leverage mathematical methods and innovations to improve efficiency in system modeling and analysis. By participating, members gain access to leading-edge methodologies and contribute to the future of MBSE standards. Contact [email protected] to join the Math DSIG and help redefine the future of systems engineering through mathematical excellence.