def test_TimeTracking():
""" Main test."""
# setup problem
mesh = fd.UnitSquareMesh(20, 20)
Q = fs.FeControlSpace(mesh)
inner = fs.LaplaceInnerProduct(Q, fixed_bids=[1, 2, 3, 4])
q = fs.ControlVector(Q, inner)
# create PDEconstrained objective functional
J = TimeTracking(Q)
# ROL parameters
params_dict = {
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 25
}
},
'Step': {
'Type': 'Trust Region'
},
'Status Test': {
'Gradient Tolerance': 1e-3,
'Step Tolerance': 1e-8,
'Iteration Limit': 20
}
}
# 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 < 1e-3)
import firedrake as fd
import fireshape as fs
import fireshape.zoo as fsz
import ROL
n = 30
# mesh = fd.UnitSquareMesh(n, n)
mesh = fd.Mesh("UnitSquareCrossed.msh")
mesh = fd.MeshHierarchy(mesh, 1)[-1]
Q = fs.FeMultiGridControlSpace(mesh, refinements=3, order=2)
inner = fs.LaplaceInnerProduct(Q)
mesh_m = Q.mesh_m
V_m = fd.FunctionSpace(mesh_m, "CG", 1)
f_m = fd.Function(V_m)
(x, y) = fd.SpatialCoordinate(mesh_m)
f = (pow(x - 0.5, 2)) + pow(y - 0.5, 2) - 2.
out = fd.File("domain.pvd")
J = fsz.LevelsetFunctional(f, Q, cb=lambda: out.write(mesh_m.coordinates))
q = fs.ControlVector(Q, inner)
params_dict = {
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 5
}
},
'Step': {
print("Harmonic map exists for r^*/R^* = %.2f" % ((0.5 * (R / r + r / R))**-1))
Rs = 1.0
rs = args.rstar
Q = fs.FeControlSpace(mesh)
d = distance_function(Q.get_space_for_inner()[0].mesh(), boundary_ids=[1, 2])
if args.weighted:
mu_base = 0.01 / (0.01 + d)
else:
mu_base = fd.Constant(1.)
# mu_base = fd.Constant(1.0)
if args.base_inner == "elasticity":
inner = fs.ElasticityInnerProduct(Q, mu=mu_base, direct_solve=True)
elif args.base_inner == "laplace":
inner = fs.LaplaceInnerProduct(Q, mu=mu_base, direct_solve=True)
else:
raise NotImplementedError
if args.alpha is not None:
mu_cr = mu_base / args.alpha
inner = CauchyRiemannAugmentation(mu_cr, inner)
mesh_m = Q.mesh_m
(x, y) = fd.SpatialCoordinate(mesh_m)
r = fd.sqrt(x**2 + y**2)
expr = (r - fd.Constant(rs)) * (r - fd.Constant(Rs))
J = 0.1 * fsz.LevelsetFunctional(expr, Q, quadrature_degree=5)
q = fs.ControlVector(Q, inner)
fd.solve(self.F(t, self.u, self.u_old) == 0, self.u, bcs=self.bcs)
t += self.dt
self.J += fd.assemble(self.dt * (self.u - self.u_t(t))**2 *
self.dx)
def objective_value(self):
"""Return the value of the objective function."""
return self.J
if __name__ == "__main__":
# setup problem
mesh = fd.UnitSquareMesh(20, 20)
Q = fs.FeControlSpace(mesh)
inner = fs.LaplaceInnerProduct(Q, fixed_bids=[1, 2, 3, 4])
q = fs.ControlVector(Q, inner)
J = TimeTracking(Q)
params_dict = {
'Step': {
'Type': 'Trust Region'
},
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 25
}
},
'Status Test': {
'Gradient Tolerance': 1e-3,
import firedrake as fd
import fireshape as fs
import fireshape.zoo as fsz
import ROL
from PDEconstraint_pipe import NavierStokesSolver
from objective_pipe import PipeObjective
# setup problem
mesh = fd.Mesh("pipe.msh")
Q = fs.FeControlSpace(mesh)
inner = fs.LaplaceInnerProduct(Q, fixed_bids=[10, 11, 12])
q = fs.ControlVector(Q, inner)
# setup PDE constraint
if mesh.topological_dimension() == 2: # in 2D
viscosity = fd.Constant(1./400.)
elif mesh.topological_dimension() == 3: # in 3D
viscosity = fd.Constant(1/10.) # simpler problem in 3D
else:
raise NotImplementedError
e = NavierStokesSolver(Q.mesh_m, viscosity)
# save state variable evolution in file u2.pvd or u3.pvd
if mesh.topological_dimension() == 2: # in 2D
out = fd.File("solution/u2D.pvd")
elif mesh.topological_dimension() == 3: # in 3D
out = fd.File("solution/u3D.pvd")
def cb():
return out.write(e.solution.split()[0])
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_box_constraint(pytestconfig):
n = 5
mesh = fd.UnitSquareMesh(n, n)
T = mesh.coordinates.copy(deepcopy=True)
(x, y) = fd.SpatialCoordinate(mesh)
T.interpolate(T + fd.Constant((1, 0)) * x * y)
mesh = fd.Mesh(T)
Q = fs.FeControlSpace(mesh)
inner = fs.LaplaceInnerProduct(Q, fixed_bids=[1])
mesh_m = Q.mesh_m
q = fs.ControlVector(Q, inner)
if pytestconfig.getoption("verbose"):
out = fd.File("domain.pvd")
def cb():
out.write(mesh_m.coordinates)
else:
def cb():
pass
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)))
J = fsz.MoYoBoxConstraint(1, [2],
Q,
lower_bound=lower_bound,
upper_bound=upper_bound,
cb=cb,
quadrature_degree=100)
g = q.clone()
J.gradient(g, q, None)
taylor_result = J.checkGradient(q, g, 9, 1)
for i in range(len(taylor_result) - 1):
if taylor_result[i][3] > 1e-7:
assert taylor_result[i + 1][3] <= taylor_result[i][3] * 0.11
params_dict = {
'Step': {
'Type': 'Line Search',
'Line Search': {
'Descent Method': {
'Type': 'Quasi-Newton Step'
}
}
},
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 2
}
},
'Status Test': {
'Gradient Tolerance': 1e-10,
'Step Tolerance': 1e-10,
'Iteration Limit': 150
}
}
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(J, q)
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
Tvec = Q.T.vector()
nodes = fd.DirichletBC(Q.V_r, fd.Constant((0.0, 0.0)), [2]).nodes
assert np.all(Tvec[nodes, 0] <= 1.3 + 1e-4)
assert np.all(Tvec[nodes, 1] <= 0.9 + 1e-4)
def test_objective_plus_box_constraint(pytestconfig):
n = 10
mesh = fd.UnitSquareMesh(n, n)
T = mesh.coordinates.copy(deepcopy=True)
(x, y) = fd.SpatialCoordinate(mesh)
T.interpolate(T + fd.Constant((0, 0)))
mesh = fd.Mesh(T)
Q = fs.FeControlSpace(mesh)
inner = fs.LaplaceInnerProduct(Q)
mesh_m = Q.mesh_m
q = fs.ControlVector(Q, inner)
if pytestconfig.getoption("verbose"):
out = fd.File("domain.pvd")
def cb():
out.write(mesh_m.coordinates)
else:
def cb():
pass
lower_bound = Q.T.copy(deepcopy=True)
lower_bound.interpolate(fd.Constant((-0.2, -0.2)))
upper_bound = Q.T.copy(deepcopy=True)
upper_bound.interpolate(fd.Constant((+1.2, +1.2)))
# levelset test case
(x, y) = fd.SpatialCoordinate(Q.mesh_m)
f = (pow(x - 0.5, 2)) + pow(y - 0.5, 2) - 4.
J1 = fsz.LevelsetFunctional(f, Q, cb=cb, quadrature_degree=10)
J2 = fsz.MoYoBoxConstraint(10., [1, 2, 3, 4],
Q,
lower_bound=lower_bound,
upper_bound=upper_bound,
cb=cb,
quadrature_degree=10)
J3 = fsz.MoYoSpectralConstraint(100,
fd.Constant(0.6),
Q,
cb=cb,
quadrature_degree=100)
J = 0.1 * J1 + J2 + J3
g = q.clone()
J.gradient(g, q, None)
taylor_result = J.checkGradient(q, g, 9, 1)
for i in range(len(taylor_result) - 1):
if taylor_result[i][3] > 1e-6 and taylor_result[i][3] < 1e-3:
assert taylor_result[i + 1][3] <= taylor_result[i][3] * 0.15
params_dict = {
'Step': {
'Type': 'Line Search',
'Line Search': {
'Descent Method': {
'Type': 'Quasi-Newton Step'
}
}
},
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 2
}
},
'Status Test': {
'Gradient Tolerance': 1e-10,
'Step Tolerance': 1e-10,
'Iteration Limit': 10
}
}
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(J, q)
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
Tvec = Q.T.vector()
nodes = fd.DirichletBC(Q.V_r, fd.Constant((0.0, 0.0)), [2]).nodes
assert np.all(Tvec[nodes, 0] <= 1.2 + 1e-1)
assert np.all(Tvec[nodes, 1] <= 1.2 + 1e-1)
def test_spectral_constraint(pytestconfig):
n = 5
mesh = fd.UnitSquareMesh(n, n)
T = fd.Function(fd.VectorFunctionSpace(
mesh, "CG",
1)).interpolate(fd.SpatialCoordinate(mesh) - fd.Constant((0.5, 0.5)))
mesh = fd.Mesh(T)
Q = fs.FeControlSpace(mesh)
inner = fs.LaplaceInnerProduct(Q)
mesh_m = Q.mesh_m
q = fs.ControlVector(Q, inner)
if pytestconfig.getoption("verbose"):
out = fd.File("domain.pvd")
def cb():
out.write(mesh_m.coordinates)
else:
def cb():
pass
J = fsz.MoYoSpectralConstraint(0.5, fd.Constant(0.1), Q, cb=cb)
q.fun += Q.T
g = q.clone()
J.update(q, None, -1)
J.gradient(g, q, None)
cb()
taylor_result = J.checkGradient(q, g, 7, 1)
for i in range(len(taylor_result) - 1):
assert taylor_result[i + 1][3] <= taylor_result[i][3] * 0.11
params_dict = {
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 2
}
},
'Step': {
'Type': 'Line Search',
'Line Search': {
'Descent Method': {
'Type': 'Quasi-Newton Step'
}
}
},
'Status Test': {
'Gradient Tolerance': 1e-10,
'Step Tolerance': 1e-10,
'Iteration Limit': 150
}
}
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(J, q)
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
Tvec = Q.T.vector()[:, :]
for i in range(Tvec.shape[0]):
assert abs(Tvec[i, 0]) < 0.55 + 1e-4
assert abs(Tvec[i, 1]) < 0.55 + 1e-4
assert np.any(np.abs(Tvec) > 0.55 - 1e-4)
use_cr = bool(args.use_cr)
base_inner = args.base_inner
mesh = fd.Mesh("Sphere2D.msh")
Q = fs.FeControlSpace(mesh)
d = distance_function(Q.get_space_for_inner()[0].mesh(), eps=fd.Constant(0.1))
mu_base = 0.01 / (0.01 + d)
if base_inner == "elasticity":
inner = fs.ElasticityInnerProduct(Q,
fixed_bids=[1, 2, 3],
mu=mu_base,
direct_solve=True)
elif base_inner == "laplace":
inner = fs.LaplaceInnerProduct(Q,
fixed_bids=[1, 2, 3],
mu=mu_base,
direct_solve=True)
else:
raise NotImplementedError
if use_cr:
mu_cr = 100.0 * mu_base
inner = CauchyRiemannAugmentation(mu_cr, inner)
mesh_m = Q.mesh_m
(x, y) = fd.SpatialCoordinate(mesh_m)
inflow_expr = fd.Constant((1.0, 0.0))
e = fsz.StokesSolver(mesh_m,
inflow_bids=[1, 2, 3],
inflow_expr=inflow_expr,
noslip_bids=[4],