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Objectives, Optimizers, and Grids

Objectives and Constraints

desc.objectives defines a number of different metrics for stellarator optimization problems, which can be used as either objectives or constraints depending on how they are passed to the optimizer. Individual objectives are combined into an ObjectiveFunction that is then passed to the Optimizer.

ObjectiveFunction

.. autosummary::
    :toctree: _api/objectives
    :recursive:
    :template: class.rst

    desc.objectives.ObjectiveFunction

Equilibrium

.. autosummary::
    :toctree: _api/objectives
    :recursive:
    :template: class.rst

    desc.objectives.ForceBalance
    desc.objectives.ForceBalanceAnisotropic
    desc.objectives.Energy
    desc.objectives.CurrentDensity
    desc.objectives.RadialForceBalance
    desc.objectives.HelicalForceBalance

Geometry

.. autosummary::
    :toctree: _api/objectives
    :recursive:
    :template: class.rst

    desc.objectives.AspectRatio
    desc.objectives.Elongation
    desc.objectives.Volume
    desc.objectives.MeanCurvature
    desc.objectives.PrincipalCurvature
    desc.objectives.PlasmaVesselDistance
    desc.objectives.BScaleLength
    desc.objectives.GoodCoordinates

Omnigenity

.. autosummary::
    :toctree: _api/objectives
    :recursive:
    :template: class.rst

    desc.objectives.QuasisymmetryTwoTerm
    desc.objectives.QuasisymmetryTripleProduct
    desc.objectives.QuasisymmetryBoozer
    desc.objectives.Omnigenity
    desc.objectives.Isodynamicity

Stability

.. autosummary::
    :toctree: _api/objectives
    :recursive:
    :template: class.rst

    desc.objectives.MagneticWell
    desc.objectives.MercierStability

Free boundary / Single stage optimization

.. autosummary::
    :toctree: _api/objectives
    :recursive:
    :template: class.rst

    desc.objectives.BoundaryError
    desc.objectives.VacuumBoundaryError

Profiles

.. autosummary::
    :toctree: _api/objectives
    :recursive:
    :template: class.rst

    desc.objectives.RotationalTransform
    desc.objectives.Shear
    desc.objectives.ToroidalCurrent
    desc.objectives.Pressure
    desc.objectives.BootstrapRedlConsistency

Fixing degrees of freedom

.. autosummary::
    :toctree: _api/objectives
    :recursive:
    :template: class.rst

    desc.objectives.FixBoundaryR
    desc.objectives.FixBoundaryZ
    desc.objectives.FixAxisR
    desc.objectives.FixAxisZ
    desc.objectives.FixPsi
    desc.objectives.FixPressure
    desc.objectives.FixIota
    desc.objectives.FixCurrent
    desc.objectives.FixAtomicNumber
    desc.objectives.FixElectronDensity
    desc.objectives.FixElectronTemperature
    desc.objectives.FixIonTemperature
    desc.objectives.FixModeR
    desc.objectives.FixModeZ
    desc.objectives.FixSumModesR
    desc.objectives.FixSumModesZ
    desc.objectives.FixThetaSFL
    desc.objectives.FixParameter

User defined objectives

.. autosummary::
    :toctree: _api/objectives
    :recursive:
    :template: class.rst


    desc.objectives.GenericObjective
    desc.objectives.ObjectiveFromUser
    desc.objectives.LinearObjectiveFromUser

Utilities for getting common groups of constraints

.. autosummary::
    :toctree: _api/objectives
    :recursive:
    :template: class.rst

    desc.objectives.get_fixed_boundary_constraints
    desc.objectives.get_NAE_constraints
    desc.objectives.get_fixed_axis_constraints
    desc.objectives.get_equilibrium_objective

Optimization

desc.optimize.Optimizer is the primary interface, it contains wrappers for a number of different methods listed in Optimizers Supported.

.. autosummary::
   :toctree: _api/optimize
   :recursive:
   :template: class.rst

   desc.optimize.Optimizer

There are also a number of optimizers written specifically for DESC that we also offer with a direct interface similar to scipy.optimize.minimize:

.. autosummary::
   :toctree: _api/optimize
   :recursive:
   :template: class.rst

   desc.optimize.lsqtr
   desc.optimize.fmintr
   desc.optimize.fmin_auglag
   desc.optimize.lsq_auglag
   desc.optimize.sgd

DESC also allows you to use custom optimizers by creating a wrapper function and registering it using desc.optimize.register_optimizer. See Adding optimizers for details

.. autosummary::
   :toctree: _api/optimize
   :recursive:
   :template: class.rst

   desc.optimize.register_optimizer

Grids

A grid defines a set of collocation nodes in computational coordinates where physics quantities are to be evaluated. DESC offers a number of options with different patterns and spacing. Each objective generally has a default grid that works for most cases, but often it is desired to specify where particular objectives should be targeted, such as targeting quasi-symmetry on particular surfaces. For this a user defined grid can be created and passed to the corresponding objective.

.. autosummary::
    :toctree: _api/grid/
    :recursive:
    :template: class.rst

    desc.grid.Grid
    desc.grid.LinearGrid
    desc.grid.QuadratureGrid
    desc.grid.ConcentricGrid

desc.grid also contains utilities for finding the most and least rational surfaces for a given iota profile, for either avoiding or analyzing rational surfaces.

.. autosummary::
    :toctree: _api/grid/
    :recursive:
    :template: class.rst

    desc.grid.find_least_rational_surfaces
    desc.grid.find_most_rational_surfaces