"""Inverse-design benchmark: score a set of evaluated designs."""
import numpy as np
from ._checks import require_finite
[docs]
def design_metrics(loss_fraction, mirror_ratio, mirror_target, aspect_ratio, aspect_target):
r"""Score designs that have been evaluated with VMEC and particle tracing.
Each design is evaluated as in the paper: its boundary is rescaled to ARIES-CS size
(minor radius 1.7 m, volume-averaged field 5.86 T) and its VMEC equilibrium is computed.
Its mirror ratio is :math:`\max |B| / \min |B|` on a 15 × 41 × 41 grid in
:math:`(s, \theta, \phi)`, and its loss fraction is that of 5,000 alpha particles born on
:math:`s = 0.1`, traced for 0.1 s.
For :math:`n` designs with loss fractions :math:`f_j`, mirror ratios :math:`R_j`, aspect
ratios :math:`A_j`, and targets :math:`R^*_j` and :math:`A^*_j`, the scores in percent are
.. math::
\text{low-loss rate}_c = \frac{100}{n} \sum_j \mathbb{1}[f_j \le c], \quad c = 0.10, 0.15,
\text{mirror constraint}_k = \frac{100}{n} \sum_j \mathbb{1}[R_j \le k R^*_j], \quad k = 1, 1.1,
\text{aspect error} = 100\, \operatorname{median}_j \frac{|A_j - A^*_j|}{A^*_j}.
Args:
loss_fraction (array_like): loss fraction of each design, shape ``(n,)``.
mirror_ratio (array_like): mirror ratio of each design, shape ``(n,)``.
mirror_target (array_like): target mirror ratio of each design, shape ``(n,)``.
aspect_ratio (array_like): aspect ratio of each design, shape ``(n,)``.
aspect_target (array_like): target aspect ratio of each design, shape ``(n,)``.
Returns:
dict: **low_loss_rate_10, low_loss_rate_15, mirror_constraint, mirror_constraint_1.1,
aspect_error_median**, the scores above, for :math:`c = 0.10, 0.15` and
:math:`k = 1, 1.1`.
Raises:
ValueError: if an input contains NaN or inf.
"""
require_finite(loss_fraction=loss_fraction, mirror_ratio=mirror_ratio, mirror_target=mirror_target,
aspect_ratio=aspect_ratio, aspect_target=aspect_target)
loss_fraction = np.asarray(loss_fraction, dtype=float)
mirror_ratio = np.asarray(mirror_ratio, dtype=float)
mirror_target = np.asarray(mirror_target, dtype=float)
aspect_ratio = np.asarray(aspect_ratio, dtype=float)
aspect_target = np.asarray(aspect_target, dtype=float)
return {
"low_loss_rate_10": 100 * np.mean(loss_fraction <= 0.10),
"low_loss_rate_15": 100 * np.mean(loss_fraction <= 0.15),
"mirror_constraint": 100 * np.mean(mirror_ratio <= mirror_target),
"mirror_constraint_1.1": 100 * np.mean(mirror_ratio <= 1.1 * mirror_target),
"aspect_error_median": 100 * np.median(np.abs(aspect_ratio - aspect_target) / aspect_target),
}
