CoupledSystems

Easily model and obtain analytic derivatives of arbitrarily complex coupled systems

Author: Taylor McDonnell

CoupledSystems is a modeling framework for easily modeling and obtaining exact derivatives of arbitrarily complex coupled systems. It is similar in nature to OpenMDAO, but relies on a different theoretical foundation for propagating derivatives (and is written in Julia!). It is also designed to automatically interface with a variety of packages in the Julia ecosystem to make obtaining derivatives and solving nonlinear systems of equations relatively painless.

Package Features

• Can be used to:
  • Perform mixed-mode automatic differentiation
  • Construct objective and constraint functions (with exact derivatives) for gradient-based optimization.
  • Easily construct monolithic coupled systems of equations from an arbitrary number of systems of equations.
  • Perform efficient sensitivity analyses and obtain exact derivatives (to machine precision)
• Automatically calculates partial derivatives using:
  • Finite Differencing (Implemented using FiniteDiff)
    • Forward
    • Central
    • Complex Step
  • Automatic Differentiation
    • Forward Mode (Implemented using ForwardDiff)
    • Reverse Mode (Implemented using ReverseDiff)
  • User-defined analytic calculations
• Automatically calculates total derivatives using the
  • Chain Rule (for explicit systems)
    • Forward
    • Reverse
  • Analytic Sensitivity Equations (for implicit systems)
    • Direct
    • Adjoint
• Multiple solvers available for solving implicit systems
  • Trust Region (Implemented using NLsolve)
  • Newton's Method with Line Search (Implemented using NLsolve)
  • User-defined solvers
• Efficient and convenient calling interface
  • Output only, derivative only, and/or combined output and derivative calculation functions
  • Non-allocating interface to reduce/eliminate run-time allocations
  • Allocating interface for derivative verification using ForwardDiff
  • Only calculates new values/derivatives for each component/subcomponent if inputs have been updated (unless otherwise specified)

Installation

Enter the package manager by typing ] and then run the following:

pkg> add CoupledSystems

Usage

See the documentation

References

[1] Martins, Joaquim R. R. A., and Ning, Andrew, Engineering Design Optimization, Cambridge University Press, 2021.