Overview
Ways to use simsopt
Simsopt is a collection of classes and functions that can be used in several ways. One application is to solve optimization problems involving stellarators, similar to STELLOPT. You could also define an objective function using simsopt, but use an optimization library outside simsopt to solve it. Or, you could use the simsopt optimization infrastructure to optimize your own objects, which may or may not have any connection to stellarators. Alternatively, you can use the stellarator-related objects in a script for some purpose other than optimization, such as plotting how some code output varies as an input parameter changes, or evaluating the finite-difference gradient of some code outputs. Or, you can manipulate the objects interactively, at the python command line or in a Jupyter notebook.
Input files
Simsopt does not use input data files to define optimization problems,
in contrast to STELLOPT
. Rather, problems are specified using a
python driver script, in which objects are defined and
configured. However, objects related to specific physics codes may use
their own input files. In particular, a simsopt.mhd.Vmec
object
can be initialized using a standard VMEC input.*
input file, and a
simsopt.mhd.Spec
object can be initialized using a standard
SPEC *.sp
input file.
Optimization stages
Recent optimized stellarators have been designed using two stages, both of which can be performed using simsopt. In the first stage, the parameter space is the shape of a toroidal boundary flux surface. Coils are not considered explicitly in this stage. The objective function involves surrogates for confinement and stability in the plasma inside the boundary surface. In the second optimization stage, coil shapes are optimized to produce the plasma shape that resulted from stage 1. The parameter space for stage 2 represents the space of coil shapes. The objective function for stage 2 usually involves several terms. One term is the deviation between the magnetic field produced by the coils and the magnetic field desired at the plasma boundary, given the stage 1 solution. Other terms in the objective function introduce regularization on the coil shapes, such as the coil length and/or curvature, and reflect other engineering considerations such as the distance between coils. In the future, we aim to introduce alternative optimization strategies in simsopt besides this two-stage approach, such as combined single-stage methods.
Optimization
To do optimization using simsopt, there are four basic steps:
Define the physical entities in the optimization problem (coils, MHD equilibria, etc.) by creating instances of the relevant simsopt classes.
Define the independent variables for the optimization, by choosing which degrees of freedom of these objects are free vs fixed.
Define an objective function.
Solve the optimization problem that has been defined.
This pattern is evident in the tutorials in this documentation
and in the examples
directory of the repository.
Some typical objects are a MHD equilibrium represented by the VMEC or
SPEC code, or some electromagnetic coils. To define objective
functions, a variety of additional objects can be defined that depend
on the MHD equilibrium or coils, such as a
simsopt.mhd.Boozer
object for Boozer-coordinate
transformation, a simsopt.mhd.Residue
object to represent
Greene’s residue of a magnetic island, or a
simsopt.geo.LpCurveCurvature
penalty on coil
curvature.
More details about setting degrees of freedom and defining objective functions can be found on the Defining optimization problems page.
For the solution step, two functions are provided presently,
simsopt.solve.least_squares_serial_solve()
and
simsopt.solve.least_squares_mpi_solve()
. The first
is simpler, while the second allows MPI-parallelized finite differences
to be used in the optimization.
Modules
Classes and functions in simsopt are organized into several modules:
simsopt.geo
contains several representations of curves and surfaces.simsopt.field
contains machinery for the Biot-Savart law and other magnetic field representations.simsopt.mhd
contains interfaces to MHD equilibrium codes and tools for diagnosing their output.simsopt.objectives
contains tools for some common objective functions.simsopt.solve
contains wrappers for some optimization algorithms.simsopt.util
contains other utility functions.simsopt._core
defines theOptimizable
class and other tools used internally in simsopt.