Decapodes

A Kelvin–Helmholtz instability, simulated by a Decapodes specification, from the compositional methods talk.

Decapodes.jl is a graphical tool for the composition of physical systems. This library includes tooling which takes advantage of the formalization of physical theories described by DEC provided by CombinatorialSpaces.jl.

Point vortices spiraling Point vortices spiraling

Links:

Project team

Project articles

  1. Currier, K., Leal, W., Rauta, G., Copeland, A., Dixon, W., & Fairbanks, J. (2026). Whitney Control Barrier Functions: A Mesh-based Geometric approach via Discrete Exterior Calculus. In IFAC. (in press).
  2. Morris, L., Baas, A., Arias, J., Gatlin, M., Patterson, E., & Fairbanks, J. P. (2024). Decapodes: A diagrammatic tool for representing, composing, and computing spatialized partial differential equations. Journal of Computational Science, 81, 102345. https://doi.org/10.1016/j.jocs.2024.102345
  3. Arlin, K., Fairbanks, J., Hosgood, T., & Patterson, E. (2024). The diagrammatic presentation of equations in categories. arXiv:2401.09751.
  4. Patterson, E., Baas, A., Hosgood, T., & Fairbanks, J. (2023). A diagrammatic view of differential equations in physics. Mathematics in Engineering, 5(2), 1–59. https://doi.org/10.3934/mine.2023036

Subproject: general categorical equations

Project Leader: Kevin Carlson at the Topos Institute

Diagrammatic Presentations of Equations Diagrammatic Presentations of Equations

Sponsors

DARPA

Decapodes has been supported by the following DARPA programs:

  • Automating Scientific Knowledge Extraction
  • Directly Computable Models
  • Automating Scientific Knowledge Extraction and Modeling