Projects

Software

Decapodes.jl

Project Leader: Luke Morris

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Decapodes.jl are 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

Links:

General Categorical Equations

Project Leader: Kevin Carlson

Diagrammatic Presentations of Equations

Decapodes Articles

  • Decapodes: A diagrammatic tool for representing, composing, and computing spatialized partial differential equations
    Luke Morris, Andrew Baas, Jesus Arias, Maia Gatlin, Evan Patterson, James P. Fairbanks
    Journal of Computational Science (2024)
    Details DOI Preprint
  • A Diagrammatic Presentation of Equations in Categories
    Kevin Arlin, James Fairbanks, Tim Hosgood, Evan Patterson
    Arxiv (2022)
    Details Preprint
  • A diagrammatic view of differential equations in physics
    Evan Patterson, Andrew Baas, Timothy Hosgood, James Fairbanks
    Mathematics in Engineering (2022)
    Details DOI Preprint
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Dynamics, Optimization and Control

Project Leader: Tyler Hanks

AlgebraicControl.jl

Model predictive control (MPC) is an optimal control technique which involves solving a sequence of constrained optimization problems across a given time horizon. We present a novel Julia library that leverages our theoretical results to automate the implementation of correct-by-construction MPC problems in software.