A new approach to modeling using categories and software, facilitating the build of advanced models like digital twins, is being developed at the moment.

During the 2023 SIAM Conference on Computational Science and Engineering, a group of researchers presented their

diagrammatic representations that provide an intuitive interface for specifying the relationships between variables in a system of equations, a method for composing systems equations into a multiphysics model using an operad of wiring diagrams, and an algorithm for deriving solvers using directed hypergraphs, yielding a method of generating executable systems from these diagrams using the operators of discrete exterior calculus on a simplicial set. The generated solvers produce numerical solutions consistent with state of the art open source tools.

As pointed out, mathematics can rarely be isomorphic to its software implementation, yet here the researchers go a long way in enabling that.

Using Julia language, the applied category theorists working on this concept wrote a software (StockFlow) which allows users to build stock-flow diagrams and do all sorts of things with them - from drawing them over to transforming them into other forms like dynamical systems and system structure diagrams, or to solving the underlying differential equations.

The team have also built software (ModelCollab) that hides all the Julia code again, enabling people that aren't educated mathematicians or computer scientists to apply this way of modeling in their work.

This fascinates me, as having a way to write and audit complex systems like digital twins using free and open-source approaches can be transformative in making them accessible for smaller organisations or developed for non-core departments in bigger organisations that up to now are the only ones with enough money or people to develop them for their key operations.

Read more on John Baez's blog.

Posted on Sunday 29 October 2023 at 07:15