desc.objectives.BoundaryError

class desc.objectives.BoundaryError(eq, field, target=None, bounds=None, weight=1, normalize=True, normalize_target=True, loss_function=None, deriv_mode='auto', s=None, q=None, source_grid=None, eval_grid=None, field_grid=None, field_fixed=False, name='Boundary error', jac_chunk_size=None, *, bs_chunk_size=None, B_plasma_chunk_size=None, **kwargs)Source 

Target for free boundary conditions on LCFS for finite beta equilibrium.

Computes the residual of the following:

𝐁ₒᵤₜ ⋅ 𝐧 = 0 𝐁ₒᵤₜ² - 𝐁ᵢₙ² - 2μ₀p = 0 μ₀∇Φ − 𝐧 × [𝐁ₒᵤₜ − 𝐁ᵢₙ]

Where 𝐁ᵢₙ is the total field inside the LCFS (from fixed boundary calculation) 𝐁ₒᵤₜ is the total field outside the LCFS (from coils and virtual casing principle), 𝐧 is the outward surface normal, p is the plasma pressure, and Φ is the surface current potential on the LCFS. All residuals are weighted by the local area element ||𝐞_θ × 𝐞_ζ|| Δθ Δζ

The third equation is only included if a sheet current is supplied by making the equilibrium.surface object a FourierCurrentPotentialField, otherwise it is trivially satisfied. If it is known that the external field accurately reproduces the target equilibrium with low normal field error and pressure at the edge is zero, then the sheet current will generally be negligible and can be omitted to save effort.

This objective also works for vacuum equilibria, though in that case VacuumBoundaryError will be much faster as it avoids the singular virtual casing integral.

Parameters:

eq (Equilibrium) – Equilibrium that will be optimized to satisfy the Objective.
field (MagneticField) – External field produced by coils.
s (int or tuple[int]) – Hyperparameter for the singular integration scheme. s is roughly equal to the size of the local singular grid with respect to the global grid. More precisely the local singular grid is an st × sz subset of the full domain (θ,ζ) ∈ [0, 2π)² of source_grid. That is a subset of source_grid.num_theta × source_grid.num_zeta*source_grid.NFP. If given an integer then st=s, sz=s, otherwise st=s[0], sz=s[1].
q (int) – Order of integration on the local singular grid.
source_grid (Grid, optional) – Collocation grid containing the nodes to evaluate at for source terms for Biot- Savart integral and where to evaluate errors. source_grid should not be stellarator symmetric, and both should be at rho=1. Defaults to LinearGrid(M=eq.M_grid, N=eq.N_grid) for both.
eval_grid (Grid, optional) – Collocation grid containing the nodes to evaluate at for source terms for Biot- Savart integral and where to evaluate errors. source_grid should not be stellarator symmetric, and both should be at rho=1. Defaults to LinearGrid(M=eq.M_grid, N=eq.N_grid) for both.
field_grid (Grid, optional) – Grid used to discretize field. Defaults to default grid for given field.
field_fixed (bool) – Whether to assume the field is fixed. For free boundary solve, should be fixed. For single stage optimization, should be False (default).
bs_chunk_size (int or None) – Size to split Biot-Savart computation into chunks of evaluation points. If no chunking should be done or the chunk size is the full input then supply None.
B_plasma_chunk_size (int or None) – Size to split singular integral computation into chunks. If no chunking should be done or the chunk size is the full input then supply None. Default is bs_chunk_size.
target ({float, ndarray}, optional) – Target value(s) of the objective. Only used if bounds is None. Must be broadcastable to Objective.dim_f. Defaults to target=0.
bounds (tuple of {float, ndarray}, optional) – Lower and upper bounds on the objective. Overrides target. Both bounds must be broadcastable to Objective.dim_f. Defaults to target=0.
weight ({float, ndarray}, optional) – Weighting to apply to the Objective, relative to other Objectives. Must be broadcastable to Objective.dim_f.
normalize (bool, optional) – Whether to compute the error in physical units or non-dimensionalize.
normalize_target (bool, optional) – Whether target and bounds should be normalized before comparing to computed values. If normalize is True and the target is in physical units, this should also be set to True.
loss_function ({None, 'mean', 'min', 'max','sum'}, optional) – Loss function to apply to the objective values once computed. This loss function is called on the raw compute value, before any shifting, scaling, or normalization.
deriv_mode ({"auto", "fwd", "rev"}) – Specify how to compute Jacobian matrix, either forward mode or reverse mode AD. auto selects forward or reverse mode based on the size of the input and output of the objective. Has no effect on self.grad or self.hess which always use reverse mode and forward over reverse mode respectively.
name (str, optional) – Name of the objective.
jac_chunk_size (int or auto, optional) – Will calculate the Jacobian jac_chunk_size columns at a time, instead of all at once. The memory usage of the Jacobian calculation is roughly memory usage = m0+m1*jac_chunk_size: the smaller the chunk size, the less memory the Jacobian calculation will require (with some baseline memory usage). The time it takes to compute the Jacobian is roughly t = t0+t1/jac_chunk_size so the larger the jac_chunk_size, the faster the calculation takes, at the cost of requiring more memory. If None, it will use the largest size i.e obj.dim_x. Can also help with Hessian computation memory, as Hessian is essentially jacfwd(jacrev(f)), and each of these operations may be chunked. Defaults to chunk_size=None. Note: When running on a CPU (not a GPU) on a HPC cluster, DESC is unable to accurately estimate the available device memory, so the auto chunk_size option will yield a larger chunk size than may be needed. It is recommended to manually choose a chunk_size if an OOM error is experienced in this case.

Examples

Assigning a surface current to the equilibrium:

from desc.magnetic_fields import FourierCurrentPotentialField
# turn the regular FourierRZToroidalSurface into a current potential on the
# last closed flux surface
eq.surface = FourierCurrentPotentialField.from_surface(eq.surface,
                                                      M_Phi=eq.M,
                                                      N_Phi=eq.N,
                                                      )
objective = BoundaryError(eq, field)

Methods

`build`([use_jit, verbose])	Build constant arrays.
`compute`(eq_params, *field_params[, constants])	Compute boundary force error.
`compute_scalar`(args, *kwargs)	Compute the scalar form of the objective.
`compute_scaled`(args, *kwargs)	Compute and apply weighting and normalization.
`compute_scaled_error`(args, *kwargs)	Compute and apply the target/bounds, weighting, and normalization.
`compute_unscaled`(args, *kwargs)	Compute the raw value of the objective.
`copy`([deepcopy])	Return a (deep)copy of this object.
`equiv`(other)	Compare equivalence between DESC objects.
`grad`(args, *kwargs)	Compute gradient vector of self.compute_scalar wrt x.
`hess`(args, *kwargs)	Compute Hessian matrix of self.compute_scalar wrt x.
`jac_scaled`(args, *kwargs)	Compute Jacobian matrix of self.compute_scaled wrt x.
`jac_scaled_error`(args, *kwargs)	Compute Jacobian matrix of self.compute_scaled_error wrt x.
`jac_unscaled`(args, *kwargs)	Compute Jacobian matrix of self.compute_unscaled wrt x.
`jvp_scaled`(v, x[, constants])	Compute Jacobian-vector product of self.compute_scaled.
`jvp_scaled_error`(v, x[, constants])	Compute Jacobian-vector product of self.compute_scaled_error.
`jvp_unscaled`(v, x[, constants])	Compute Jacobian-vector product of self.compute_unscaled.
`load`(load_from[, file_format])	Initialize from file.
`print_value`(args[, args0])	Print the value of the objective and return a dict of values.
`save`(file_name[, file_format, file_mode])	Save the object.
`xs`(*things)	Return a tuple of args required by this objective from optimizable things.

Attributes

`bounds`	Lower and upper bounds of the objective.
`built`	Whether the transforms have been precomputed (or not).
`constants`	Constant parameters such as transforms and profiles.
`dim_f`	Number of objective equations.
`fixed`	Whether the objective fixes individual parameters (or linear combo).
`linear`	Whether the objective is a linear function (or nonlinear).
`name`	Name of objective (str).
`normalization`	normalizing scale factor.
`scalar`	Whether default "compute" method is a scalar or vector.
`target`	Target value(s) of the objective.
`things`	Optimizable things that this objective is tied to.
`weight`	Weighting to apply to the Objective, relative to other Objectives.