Coil forces

.github/workflows/extensive_test.yml

@@ -29,7 +29,7 @@ jobs:
       matrix:
         test-type: [unit, integrated]
         packages: [all, vmec, spec, none]
-        python-version: [3.8, 3.9, "3.10"]
+        python-version: [3.9, "3.10", "3.11"]
         include:
             - python-version: 3.9
               test-type: unit

.gitmodules

@@ -18,4 +18,4 @@
 	url = https://gitlab.com/libeigen/eigen.git
 [submodule "thirdparty/fmt"]
 	path = thirdparty/fmt
-	url = https://github.com/fmtlib/fmt.git
+	url = https://github.com/fmtlib/fmt.git

examples/3_Advanced/coil_forces.py

@@ -0,0 +1,207 @@
+#!/usr/bin/env python
+
+"""
+Example script for the force metric in a stage-two coil optimization
+"""
+import os
+from pathlib import Path
+from scipy.optimize import minimize
+import numpy as np
+from simsopt.geo import curves_to_vtk, create_equally_spaced_curves
+from simsopt.geo import SurfaceRZFourier
+from simsopt.field import Current, coils_via_symmetries
+from simsopt.objectives import SquaredFlux, Weight, QuadraticPenalty
+from simsopt.geo import (CurveLength, CurveCurveDistance, CurveSurfaceDistance, 
+                         MeanSquaredCurvature, LpCurveCurvature)
+from simsopt.field import BiotSavart
+from simsopt.field.force import coil_force, LpCurveForce
+from simsopt.field.selffield import regularization_circ
+from simsopt.util import in_github_actions
+
+
+###############################################################################
+# INPUT PARAMETERS
+###############################################################################
+
+# Number of unique coil shapes, i.e. the number of coils per half field period:
+# (Since the configuration has nfp = 2, multiply by 4 to get the total number of coils.)
+ncoils = 4
+
+# Major radius for the initial circular coils:
+R0 = 1.0
+
+# Minor radius for the initial circular coils:
+R1 = 0.5
+
+# Number of Fourier modes describing each Cartesian component of each coil:
+order = 5
+
+# Weight on the curve lengths in the objective function. We use the `Weight`
+# class here to later easily adjust the scalar value and rerun the optimization
+# without having to rebuild the objective.
+LENGTH_WEIGHT = Weight(1e-03)
+LENGTH_TARGET = 17.4
+
+# Threshold and weight for the coil-to-coil distance penalty in the objective function:
+CC_THRESHOLD = 0.1
+CC_WEIGHT = 1000
+
+# Threshold and weight for the coil-to-surface distance penalty in the objective function:
+CS_THRESHOLD = 0.3
+CS_WEIGHT = 10
+
+# Threshold and weight for the curvature penalty in the objective function:
+CURVATURE_THRESHOLD = 5.
+CURVATURE_WEIGHT = 1e-6
+
+# Threshold and weight for the mean squared curvature penalty in the objective function:
+MSC_THRESHOLD = 5
+MSC_WEIGHT = 1e-6
+
+# Weight on the mean squared force penalty in the objective function
+FORCE_WEIGHT = Weight(1e-26)
+
+# Number of iterations to perform:
+MAXITER = 50 if in_github_actions else 400
+
+# File for the desired boundary magnetic surface:
+TEST_DIR = (Path(__file__).parent / ".." / ".." / "tests" / "test_files").resolve()
+filename = TEST_DIR / 'input.LandremanPaul2021_QA'
+
+# Directory for output
+OUT_DIR = "./output/"
+os.makedirs(OUT_DIR, exist_ok=True)
+
+
+###############################################################################
+# SET UP OBJECTIVE FUNCTION
+###############################################################################
+
+# Initialize the boundary magnetic surface:
+nphi = 32
+ntheta = 32
+s = SurfaceRZFourier.from_vmec_input(filename, range="half period", nphi=nphi, ntheta=ntheta)
+
+# Create the initial coils:
+base_curves = create_equally_spaced_curves(ncoils, s.nfp, stellsym=True, R0=R0, R1=R1, order=order)
+base_currents = [Current(1e5) for i in range(ncoils)]
+# Since the target field is zero, one possible solution is just to set all
+# currents to 0. To avoid the minimizer finding that solution, we fix one
+# of the currents:
+base_currents[0].fix_all()
+
+coils = coils_via_symmetries(base_curves, base_currents, s.nfp, True)
+base_coils = coils[:ncoils]
+bs = BiotSavart(coils)
+bs.set_points(s.gamma().reshape((-1, 3)))
+
+curves = [c.curve for c in coils]
+curves_to_vtk(curves, OUT_DIR + "curves_init", close=True)
+pointData = {"B_N": np.sum(bs.B().reshape((nphi, ntheta, 3)) * s.unitnormal(), axis=2)[:, :, None]}
+s.to_vtk(OUT_DIR + "surf_init", extra_data=pointData)
+
+# Define the individual terms objective function:
+Jf = SquaredFlux(s, bs)
+Jls = [CurveLength(c) for c in base_curves]
+Jccdist = CurveCurveDistance(curves, CC_THRESHOLD, num_basecurves=ncoils)
+Jcsdist = CurveSurfaceDistance(curves, s, CS_THRESHOLD)
+Jcs = [LpCurveCurvature(c, 2, CURVATURE_THRESHOLD) for c in base_curves]
+Jmscs = [MeanSquaredCurvature(c) for c in base_curves]
+Jforce = [LpCurveForce(c, coils, regularization_circ(0.05), p=4) for c in base_coils]
+# Jforce = [MeanSquaredForce(c, coils, regularization_circ(0.05)) for c in base_coils]
+
+
+# Form the total objective function. To do this, we can exploit the
+# fact that Optimizable objects with J() and dJ() functions can be
+# multiplied by scalars and added:
+JF = Jf \
+    + LENGTH_WEIGHT * QuadraticPenalty(sum(Jls), LENGTH_TARGET, "max") \
+    + CC_WEIGHT * Jccdist \
+    + CS_WEIGHT * Jcsdist \
+    + CURVATURE_WEIGHT * sum(Jcs) \
+    + MSC_WEIGHT * sum(QuadraticPenalty(J, MSC_THRESHOLD, "max") for J in Jmscs) \
+    + FORCE_WEIGHT * sum(Jforce)
+
+# We don't have a general interface in SIMSOPT for optimisation problems that
+# are not in least-squares form, so we write a little wrapper function that we
+# pass directly to scipy.optimize.minimize
+
+
+def fun(dofs):
+    JF.x = dofs
+    J = JF.J()
+    grad = JF.dJ()
+    return J, grad
+
+
+# print("""
+# ###############################################################################
+# # Perform a Taylor test
+# ###############################################################################
+# """)
+# print("(It make take jax several minutes to compile the objective for the first evaluation.)")
+# f = fun
+# dofs = JF.x
+# np.random.seed(1)
+# h = np.random.uniform(size=dofs.shape)
+# J0, dJ0 = f(dofs)
+# dJh = sum(dJ0 * h)
+# for eps in [1e-3, 1e-4, 1e-5, 1e-6, 1e-7]:
+#     J1, _ = f(dofs + eps*h)
+#     J2, _ = f(dofs - eps*h)
+#     print("err", (J1-J2)/(2*eps) - dJh)
+
+###############################################################################
+# RUN THE OPTIMIZATION
+###############################################################################
+
+
+def pointData_forces(coils):
+    forces = []
+    for c in coils:
+        force = np.linalg.norm(coil_force(c, coils, regularization_circ(0.05)), axis=1)
+        force = np.append(force, force[0])
+        forces = np.concatenate([forces, force])
+    point_data = {"F": forces}
+    return point_data
+
+
+dofs = JF.x
+print(f"Optimization with FORCE_WEIGHT={FORCE_WEIGHT.value} and LENGTH_WEIGHT={LENGTH_WEIGHT.value}")
+# print("INITIAL OPTIMIZATION")
+res = minimize(fun, dofs, jac=True, method='L-BFGS-B', options={'maxiter': MAXITER, 'maxcor': 300}, tol=1e-15)
+curves_to_vtk(curves, OUT_DIR + "curves_opt_short", close=True, extra_data=pointData_forces(coils))
+pointData_surf = {"B_N": np.sum(bs.B().reshape((nphi, ntheta, 3)) * s.unitnormal(), axis=2)[:, :, None]}
+s.to_vtk(OUT_DIR + "surf_opt_short", extra_data=pointData_surf)
+
+# We now use the result from the optimization as the initial guess for a
+# subsequent optimization with reduced penalty for the coil length. This will
+# result in slightly longer coils but smaller `B·n` on the surface.
+dofs = res.x
+LENGTH_WEIGHT *= 0.1
+# print("OPTIMIZATION WITH REDUCED LENGTH PENALTY\n")
+res = minimize(fun, dofs, jac=True, method='L-BFGS-B', options={'maxiter': MAXITER, 'maxcor': 300}, tol=1e-15)
+curves_to_vtk(curves, OUT_DIR + f"curves_opt_force_FWEIGHT={FORCE_WEIGHT.value:e}_LWEIGHT={LENGTH_WEIGHT.value*10:e}", close=True, extra_data=pointData_forces(coils))
+pointData_surf = {"B_N": np.sum(bs.B().reshape((nphi, ntheta, 3)) * s.unitnormal(), axis=2)[:, :, None]}
+s.to_vtk(OUT_DIR + f"surf_opt_force_WEIGHT={FORCE_WEIGHT.value:e}_LWEIGHT={LENGTH_WEIGHT.value*10:e}", extra_data=pointData_surf)
+
+# Save the optimized coil shapes and currents so they can be loaded into other scripts for analysis:
+bs.save(OUT_DIR + "biot_savart_opt.json")
+
+#Print out final important info:
+JF.x = dofs
+J = JF.J()
+grad = JF.dJ()
+jf = Jf.J()
+BdotN = np.mean(np.abs(np.sum(bs.B().reshape((nphi, ntheta, 3)) * s.unitnormal(), axis=2)))
+force = [np.max(np.linalg.norm(coil_force(c, coils, regularization_circ(0.05)), axis=1)) for c in base_coils]
+outstr = f"J={J:.1e}, Jf={jf:.1e}, ⟨B·n⟩={BdotN:.1e}"
+cl_string = ", ".join([f"{J.J():.1f}" for J in Jls])
+kap_string = ", ".join(f"{np.max(c.kappa()):.1f}" for c in base_curves)
+msc_string = ", ".join(f"{J.J():.1f}" for J in Jmscs)
+jforce_string = ", ".join(f"{J.J():.2e}" for J in Jforce)
+force_string = ", ".join(f"{f:.2e}" for f in force)
+outstr += f", Len=sum([{cl_string}])={sum(J.J() for J in Jls):.1f}, ϰ=[{kap_string}], ∫ϰ²/L=[{msc_string}], Jforce=[{jforce_string}], force=[{force_string}]"
+outstr += f", C-C-Sep={Jccdist.shortest_distance():.2f}, C-S-Sep={Jcsdist.shortest_distance():.2f}"
+outstr += f", ║∇J║={np.linalg.norm(grad):.1e}"
+print(outstr)

examples/run_serial_examples

@@ -24,3 +24,4 @@ set -ex
 ./2_Intermediate/permanent_magnet_QA.py
 ./2_Intermediate/permanent_magnet_PM4Stell.py
 ./3_Advanced/stage_two_optimization_finitebuild.py
+./3_Advanced/coil_forces.py

src/simsopt/field/__init__.py

@@ -6,6 +6,7 @@
 from .mgrid import *
 from .normal_field import *
 from .tracing import *
+from .selffield import *
 from .magnetic_axis_helpers import *
 
 __all__ = (
@@ -17,5 +18,6 @@
     + mgrid.__all__
     + normal_field.__all__
     + tracing.__all__
+    + selffield.__all__
     + magnetic_axis_helpers.__all__
 )

src/simsopt/field/coil.py

@@ -93,7 +93,6 @@ def __init__(self, current, dofs=None, **kwargs):
 
     def vjp(self, v_current):
         return Derivative({self: v_current})
-
     @property
     def current(self):
         return self.get_value()