def test_levelset(dim, inner_t, controlspace_t, use_extension, pytestconfig):
verbose = pytestconfig.getoption("verbose")
""" Test template for fsz.LevelsetFunctional."""
clscale = 0.1 if dim == 2 else 0.2
# make the mesh a bit coarser if we are using a multigrid control space as
# we are refining anyway
if controlspace_t == fs.FeMultiGridControlSpace:
clscale *= 4
if dim == 2:
mesh = fs.DiskMesh(clscale)
elif dim == 3:
mesh = fs.SphereMesh(clscale)
else:
raise NotImplementedError
if controlspace_t == fs.BsplineControlSpace:
if dim == 2:
bbox = [(-2, 2), (-2, 2)]
orders = [2, 2]
levels = [4, 4]
else:
bbox = [(-3, 3), (-3, 3), (-3, 3)]
orders = [2, 2, 2]
levels = [3, 3, 3]
Q = fs.BsplineControlSpace(mesh, bbox, orders, levels)
elif controlspace_t == fs.FeMultiGridControlSpace:
Q = fs.FeMultiGridControlSpace(mesh, refinements=1, order=2)
else:
Q = controlspace_t(mesh)
inner = inner_t(Q)
# if running with -v or --verbose, then export the shapes
if verbose:
out = fd.File("domain.pvd")
def cb(*args):
out.write(Q.mesh_m.coordinates)
cb()
else:
cb = None
# levelset test case
if dim == 2:
(x, y) = fd.SpatialCoordinate(Q.mesh_m)
f = (pow(x, 2)) + pow(1.3 * y, 2) - 1.
elif dim == 3:
(x, y, z) = fd.SpatialCoordinate(Q.mesh_m)
f = (pow(x, 2)) + pow(0.8 * y, 2) + pow(1.3 * z, 2) - 1.
else:
raise NotImplementedError
J = fsz.LevelsetFunctional(f, Q, cb=cb, scale=0.1)
if use_extension == "w_ext":
ext = fs.ElasticityExtension(Q.V_r)
if use_extension == "w_ext_fixed_dim":
ext = fs.ElasticityExtension(Q.V_r, fixed_dims=[0])
else:
ext = None
q = fs.ControlVector(Q, inner, boundary_extension=ext)
# these tolerances are not very stringent, but solutions are correct with
# tighter tolerances, the combination
# FeMultiGridControlSpace-ElasticityInnerProduct fails because the mesh
# self-intersects (one should probably be more careful with the opt params)
grad_tol = 1e-1
itlim = 15
itlimsub = 15
# Volume constraint
vol = fsz.LevelsetFunctional(fd.Constant(1.0), Q, scale=1)
initial_vol = vol.value(q, None)
econ = fs.EqualityConstraint([vol], target_value=[initial_vol])
emul = ROL.StdVector(1)
# ROL parameters
params_dict = {
'Step': {
'Type': 'Augmented Lagrangian',
'Augmented Lagrangian': {
'Subproblem Step Type': 'Line Search',
'Penalty Parameter Growth Factor': 1.05,
'Print Intermediate Optimization History': True,
'Subproblem Iteration Limit': itlimsub
},
'Line Search': {
'Descent Method': {
'Type': 'Quasi-Newton Step'
}
},
},
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 50
}
},
'Status Test': {
'Gradient Tolerance': grad_tol,
'Step Tolerance': 1e-10,
'Iteration Limit': itlim
}
}
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(J, q, econ=econ, emul=emul)
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
# verify that the norm of the gradient at optimum is small enough
# and that the volume has not changed too much
state = solver.getAlgorithmState()
assert (state.gnorm < grad_tol)
assert abs(vol.value(q, None) - initial_vol) < 1e-2
import firedrake as fd
import fireshape as fs
import fireshape.zoo as fsz
import ROL
dim = 2
mesh = fs.DiskMesh(0.4)
Q = fs.FeMultiGridControlSpace(mesh, refinements=4, order=2)
# Q = fs.FeControlSpace(mesh)
# inner = fs.SurfaceInnerProduct(Q)
inner = fs.ElasticityInnerProduct(Q)
extension = fs.ElasticityExtension(Q.V_r, direct_solve=True)
mesh_m = Q.mesh_m
if dim == 2:
(x, y) = fd.SpatialCoordinate(mesh_m)
f = (pow(x, 2)) + pow(0.5 * y, 2) - 1.
else:
(x, y, z) = fd.SpatialCoordinate(mesh_m)
f = (pow(x - 0.5, 2)) + pow(y - 0.5, 2) + pow(z - 0.5, 2) - 2.
q = fs.ControlVector(Q, inner, boundary_extension=extension)
out = fd.File("domain.pvd")
J = fsz.LevelsetFunctional(f, Q, cb=lambda: out.write(mesh_m.coordinates))
J.cb()
g = q.clone()
J.update(q, None, 1)
J.gradient(g, q, None)
g.scale(-0.3)
J.update(g, None, 1)
def test_periodic(dim, inner_t, use_extension, pytestconfig):
verbose = pytestconfig.getoption("verbose")
""" Test template for PeriodicControlSpace."""
if dim == 2:
mesh = fd.PeriodicUnitSquareMesh(30, 30)
elif dim == 3:
mesh = fd.PeriodicUnitCubeMesh(20, 20, 20)
else:
raise NotImplementedError
Q = fs.FeControlSpace(mesh)
inner = inner_t(Q)
# levelset test case
V = fd.FunctionSpace(Q.mesh_m, "DG", 0)
sigma = fd.Function(V)
if dim == 2:
x, y = fd.SpatialCoordinate(Q.mesh_m)
g = fd.sin(y * np.pi) # truncate at bdry
f = fd.cos(2 * np.pi * x) * g
perturbation = 0.05 * fd.sin(x * np.pi) * g**2
sigma.interpolate(g * fd.cos(2 * np.pi * x * (1 + perturbation)))
elif dim == 3:
x, y, z = fd.SpatialCoordinate(Q.mesh_m)
g = fd.sin(y * np.pi) * fd.sin(z * np.pi) # truncate at bdry
f = fd.cos(2 * np.pi * x) * g
perturbation = 0.05 * fd.sin(x * np.pi) * g**2
sigma.interpolate(g * fd.cos(2 * np.pi * x * (1 + perturbation)))
else:
raise NotImplementedError
class LevelsetFct(fs.ShapeObjective):
def __init__(self, sigma, f, *args, **kwargs):
super().__init__(*args, **kwargs)
self.sigma = sigma # initial
self.f = f # target
Vdet = fd.FunctionSpace(Q.mesh_r, "DG", 0)
self.detDT = fd.Function(Vdet)
def value_form(self):
# volume integral
self.detDT.interpolate(fd.det(fd.grad(self.Q.T)))
if min(self.detDT.vector()) > 0.05:
integrand = (self.sigma - self.f)**2
else:
integrand = np.nan * (self.sigma - self.f)**2
return integrand * fd.dx(metadata={"quadrature_degree": 1})
# if running with -v or --verbose, then export the shapes
if verbose:
out = fd.File("sigma.pvd")
def cb(*args):
out.write(sigma)
else:
cb = None
J = LevelsetFct(sigma, f, Q, cb=cb)
if use_extension == "w_ext":
ext = fs.ElasticityExtension(Q.V_r)
if use_extension == "w_ext_fixed_dim":
ext = fs.ElasticityExtension(Q.V_r, fixed_dims=[0])
else:
ext = None
q = fs.ControlVector(Q, inner, boundary_extension=ext)
"""
move mesh a bit to check that we are not doing the
taylor test in T=id
"""
g = q.clone()
J.gradient(g, q, None)
q.plus(g)
J.update(q, None, 1)
""" Start taylor test """
J.gradient(g, q, None)
res = J.checkGradient(q, g, 5, 1)
errors = [l[-1] for l in res]
assert (errors[-1] < 0.11 * errors[-2])
q.scale(0)
""" End taylor test """
# ROL parameters
grad_tol = 1e-4
params_dict = {
'Step': {
'Type': 'Trust Region'
},
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 25
}
},
'Status Test': {
'Gradient Tolerance': grad_tol,
'Step Tolerance': 1e-10,
'Iteration Limit': 40
}
}
# assemble and solve ROL optimization problem
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(J, q)
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
# verify that the norm of the gradient at optimum is small enough
state = solver.getAlgorithmState()
assert (state.gnorm < grad_tol)
def test_regularization(controlspace_t, use_extension):
n = 10
mesh = fd.UnitSquareMesh(n, n)
if controlspace_t == fs.FeMultiGridControlSpace:
Q = fs.FeMultiGridControlSpace(mesh, refinements=1, order=2)
else:
Q = controlspace_t(mesh)
if use_extension:
inner = fs.SurfaceInnerProduct(Q)
ext = fs.ElasticityExtension(Q.V_r)
else:
inner = fs.LaplaceInnerProduct(Q)
ext = None
q = fs.ControlVector(Q, inner, boundary_extension=ext)
X = fd.SpatialCoordinate(mesh)
q.fun.interpolate(0.5 * X)
lower_bound = Q.T.copy(deepcopy=True)
lower_bound.interpolate(fd.Constant((-0.0, -0.0)))
upper_bound = Q.T.copy(deepcopy=True)
upper_bound.interpolate(fd.Constant((+1.3, +0.9)))
J1 = fsz.MoYoBoxConstraint(1, [1, 2, 3, 4],
Q,
lower_bound=lower_bound,
upper_bound=upper_bound)
J2 = fsz.MoYoSpectralConstraint(1, fd.Constant(0.2), Q)
J3 = fsz.DeformationRegularization(Q,
l2_reg=.1,
sym_grad_reg=1.,
skew_grad_reg=.5)
if isinstance(Q, fs.FeMultiGridControlSpace):
J4 = fsz.CoarseDeformationRegularization(Q,
l2_reg=.1,
sym_grad_reg=1.,
skew_grad_reg=.5)
Js = 0.1 * J1 + J2 + 2. * (J3 + J4)
else:
Js = 0.1 * J1 + J2 + 2. * J3
g = q.clone()
def run_taylor_test(J):
J.update(q, None, 1)
J.gradient(g, q, None)
return J.checkGradient(q, g, 7, 1)
def check_result(test_result):
for i in range(len(test_result) - 1):
assert test_result[i + 1][3] <= test_result[i][3] * 0.11
check_result(run_taylor_test(J1))
check_result(run_taylor_test(J2))
check_result(run_taylor_test(J3))
if isinstance(Q, fs.FeMultiGridControlSpace):
check_result(run_taylor_test(J4))
check_result(run_taylor_test(Js))
def test_levelset(dim, inner_t, controlspace_t, use_extension, pytestconfig):
verbose = pytestconfig.getoption("verbose")
""" Test template for fsz.LevelsetFunctional."""
clscale = 0.1 if dim == 2 else 0.2
# make the mesh a bit coarser if we are using a multigrid control space as
# we are refining anyway
if controlspace_t == fs.FeMultiGridControlSpace:
clscale *= 2
if dim == 2:
mesh = fs.DiskMesh(clscale)
elif dim == 3:
mesh = fs.SphereMesh(clscale)
else:
raise NotImplementedError
if controlspace_t == fs.BsplineControlSpace:
if dim == 2:
bbox = [(-2, 2), (-2, 2)]
orders = [2, 2]
levels = [4, 4]
else:
bbox = [(-3, 3), (-3, 3), (-3, 3)]
orders = [2, 2, 2]
levels = [3, 3, 3]
Q = fs.BsplineControlSpace(mesh, bbox, orders, levels)
elif controlspace_t == fs.FeMultiGridControlSpace:
Q = fs.FeMultiGridControlSpace(mesh, refinements=1, order=2)
else:
Q = controlspace_t(mesh)
inner = inner_t(Q)
# if running with -v or --verbose, then export the shapes
if verbose:
out = fd.File("domain.pvd")
def cb(*args):
out.write(Q.mesh_m.coordinates)
cb()
else:
cb = None
# levelset test case
if dim == 2:
(x, y) = fd.SpatialCoordinate(Q.mesh_m)
f = (pow(x, 2)) + pow(1.3 * y, 2) - 1.
elif dim == 3:
(x, y, z) = fd.SpatialCoordinate(Q.mesh_m)
f = (pow(x, 2)) + pow(0.8 * y, 2) + pow(1.3 * z, 2) - 1.
else:
raise NotImplementedError
J = fsz.LevelsetFunctional(f, Q, cb=cb, scale=0.1)
if use_extension == "w_ext":
ext = fs.ElasticityExtension(Q.V_r)
if use_extension == "w_ext_fixed_dim":
ext = fs.ElasticityExtension(Q.V_r, fixed_dims=[0])
else:
ext = None
q = fs.ControlVector(Q, inner, boundary_extension=ext)
"""
move mesh a bit to check that we are not doing the
taylor test in T=id
"""
g = q.clone()
J.gradient(g, q, None)
q.plus(g)
J.update(q, None, 1)
""" Start taylor test """
J.gradient(g, q, None)
res = J.checkGradient(q, g, 5, 1)
errors = [l[-1] for l in res]
assert (errors[-1] < 0.11 * errors[-2])
q.scale(0)
""" End taylor test """
grad_tol = 1e-6 if dim == 2 else 1e-4
# ROL parameters
params_dict = {
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 50
}
},
'Step': {
'Type': 'Line Search',
'Line Search': {
'Descent Method': {
'Type': 'Quasi-Newton Step'
}
}
},
'Status Test': {
'Gradient Tolerance': grad_tol,
'Step Tolerance': 1e-10,
'Iteration Limit': 150
}
}
# assemble and solve ROL optimization problem
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(J, q)
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
# verify that the norm of the gradient at optimum is small enough
state = solver.getAlgorithmState()
assert (state.gnorm < grad_tol)