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152 | import numpy as np
from py_diff_stokes_flow.env.env_base import EnvBase
from py_diff_stokes_flow.common.common import ndarray
class FlowAveragerEnv3d(EnvBase):
def __init__(self, seed, folder):
np.random.seed(seed)
cell_nums = (64, 64, 4)
E = 100
nu = 0.499
vol_tol = 1e-2
edge_sample_num = 2
EnvBase.__init__(self, cell_nums, E, nu, vol_tol, edge_sample_num, folder)
# Initialize the parametric shapes.
self._parametric_shape_info = [ ('bezier', 11), ('bezier', 11), ('bezier', 11), ('bezier', 11) ]
# Initialize the node conditions.
self._node_boundary_info = []
inlet_range = ndarray([
[0.1, 0.4],
[0.6, 0.9],
])
outlet_range = ndarray([
[0.2, 0.4],
[0.6, 0.8]
])
cx, cy, _ = self.cell_nums()
nx, ny, nz = self.node_nums()
inlet_bd = inlet_range * cy
outlet_bd = outlet_range * cy
for j in range(ny):
for k in range(nz):
# Set the inlet at i = 0.
if inlet_bd[0, 0] < j < inlet_bd[0, 1]:
self._node_boundary_info.append(((0, j, k, 0), 1))
self._node_boundary_info.append(((0, j, k, 1), 0))
self._node_boundary_info.append(((0, j, k, 2), 0))
if inlet_bd[1, 0] < j < inlet_bd[1, 1]:
self._node_boundary_info.append(((0, j, k, 0), 0))
self._node_boundary_info.append(((0, j, k, 1), 0))
self._node_boundary_info.append(((0, j, k, 2), 0))
# Set the top and bottom plane.
for i in range(nx):
for j in range(ny):
for k in [0, nz - 1]:
self._node_boundary_info.append(((i, j, k, 2), 0))
# Initialize the interface.
self._interface_boundary_type = 'free-slip'
# Other data members.
self._inlet_range = inlet_range
self._outlet_range = outlet_range
self._inlet_bd = inlet_bd
self._outlet_bd = outlet_bd
def _variables_to_shape_params(self, x):
x = ndarray(x).copy().ravel()
assert x.size == 8
cx, cy, _ = self._cell_nums
lower = ndarray([
[1, self._outlet_range[0, 0]],
x[2:4],
x[:2],
[0, self._inlet_range[0, 0]],
])
right = ndarray([
[1, self._outlet_range[1, 0]],
[x[4], 1 - x[5]],
x[4:6],
[1, self._outlet_range[0, 1]],
])
upper = ndarray([
[0, self._inlet_range[1, 1]],
[x[0], 1 - x[1]],
[x[2], 1 - x[3]],
[1, self._outlet_range[1, 1]],
])
left = ndarray([
[0, self._inlet_range[0, 1]],
x[6:8],
[x[6], 1 - x[7]],
[0, self._inlet_range[1, 0]],
])
cxy = ndarray([cx, cy])
lower *= cxy
right *= cxy
upper *= cxy
left *= cxy
params = np.concatenate([lower.ravel(),
[0, -0.01, 1],
right.ravel(),
[0.01, 0, 1],
upper.ravel(),
[0, 0.01, 1],
left.ravel(),
[-0.01, 0, 1]
])
# Jacobian.
J = np.zeros((params.size, x.size))
J[2, 2] = J[3, 3] = 1
J[4, 0] = J[5, 1] = 1
J[13, 4] = 1
J[14, 5] = -1
J[15, 4] = J[16, 5] = 1
J[24, 0] = 1
J[25, 1] = -1
J[26, 2] = 1
J[27, 3] = -1
J[35, 6] = J[36, 7] = 1
J[37, 6] = 1
J[38, 7] = -1
J[:, ::2] *= cx
J[:, 1::2] *= cy
return ndarray(params).copy(), ndarray(J).copy()
def _loss_and_grad_on_velocity_field(self, u):
u_field = self.reshape_velocity_field(u)
grad = np.zeros(u_field.shape)
nx, ny, nz = self.node_nums()
loss = 0
cnt = 0
for j in range(ny):
for k in range(nz):
if self._outlet_bd[0, 0] < j < self._outlet_bd[0, 1] or \
self._outlet_bd[1, 0] < j < self._outlet_bd[1, 1]:
cnt += 1
u_diff = u_field[nx - 1, j, k] - ndarray([0.5, 0, 0])
loss += u_diff.dot(u_diff)
grad[nx - 1, j, k] += 2 * u_diff
loss /= cnt
grad /= cnt
return loss, ndarray(grad).ravel()
def _color_velocity(self, u):
return float(np.linalg.norm(u) / 3)
def sample(self):
return np.random.uniform(low=self.lower_bound(), high=self.upper_bound())
def lower_bound(self):
return ndarray([.01, .01, .49, .01, .49, .01, .01, .01])
def upper_bound(self):
return ndarray([.49, .49, .99, .49, .99, .49, .49, .49])
|