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149 | import numpy as np
from py_diff_stokes_flow.env.env_base import EnvBase
from py_diff_stokes_flow.common.common import ndarray
class FunnelEnv3d(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) ]
# Initialize the node conditions.
self._node_boundary_info = []
inlet_range = ndarray([0.4, 0.6])
outlet_range = 0.8
cx, cy, _ = self.cell_nums()
assert cx == cy
nx, ny, nz = self.node_nums()
inlet_bd = inlet_range * cx
outlet_bd = outlet_range * cx
inlet_velocity = ndarray([1.0, 0.0])
for j in range(ny):
for k in range(nz):
# Set the inlet at i = 0.
if inlet_bd[0] < j < inlet_bd[1]:
self._node_boundary_info.append(((0, j, k, 0), inlet_velocity[0]))
self._node_boundary_info.append(((0, j, k, 1), 0))
self._node_boundary_info.append(((0, j, k, 2), 0))
self._node_boundary_info.append(((j, 0, k, 0), inlet_velocity[1]))
self._node_boundary_info.append(((j, 0, k, 1), 0))
self._node_boundary_info.append(((j, 0, 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
self._inlet_velocity = inlet_velocity
def _variables_to_shape_params(self, x):
x = ndarray(x).copy().ravel()
assert x.size == 5
cx, cy, _ = self._cell_nums
assert cx == cy
lower_left = ndarray([
[self._inlet_range[0], 0],
[x[4], x[0]],
[x[0], x[4]],
[0, self._inlet_range[0]]
])
right = ndarray([
[1., self._outlet_range],
[x[2], x[3]],
[self._inlet_range[1], x[1]],
[self._inlet_range[1], 0]
])
upper = ndarray([
[0, self._inlet_range[1]],
[x[1], self._inlet_range[1]],
[x[3], x[2]],
[self._outlet_range, 1.]
])
lower_left *= cx
right *= cx
upper *= cx
params = np.concatenate([lower_left.ravel(),
[-0.01, -0.01, 1],
right.ravel(),
[0.01, 0, 1],
upper.ravel(),
[0, 0.01, 1],
])
# Jacobian.
J = np.zeros((params.size, x.size))
J[2, 4] = J[3, 0] = 1
J[4, 0] = J[5, 4] = 1
J[13, 2] = J[14, 3] = 1
J[16, 1] = 1
J[24, 1] = J[26, 3] = J[27, 2] = 1
J *= cx
return ndarray(params).copy(), ndarray(J).copy()
def _loss_and_grad(self, scene, u):
param_size = self._variables_to_shape_params(self.lower_bound())[0].size
grad_param = ndarray(np.zeros(param_size))
u_field = self.reshape_velocity_field(u)
grad = np.zeros(u_field.shape)
nx, ny, nz = self.node_nums()
assert nx == ny
loss = 0
cnt = 0
outlet_bd = int(np.ceil(self._outlet_range * nx))
eps = 1e-8
outlet_idx = []
for j in range(outlet_bd, ny):
for k in range(nz):
outlet_idx.append((nx - 1, j, k))
for i in range(outlet_bd, nx):
for k in range(nz):
outlet_idx.append((i, ny - 1, k))
for i, j, k in outlet_idx:
cnt += 1
ux, uy, _ = u_field[i, j, k]
angle = np.arctan2(uy, ux)
loss += np.abs(angle - np.pi / 4)
dangle_ux = -uy / (ux ** 2 + uy ** 2 + eps)
dangle_uy = ux / (ux ** 2 + uy ** 2 + eps)
grad[i, j, k] += ndarray([
np.sign(angle - np.pi / 4) * dangle_ux,
np.sign(angle - np.pi / 4) * dangle_uy,
0
])
loss /= cnt
grad /= cnt
return loss, ndarray(grad).ravel(), grad_param
def _color_velocity(self, u):
return float(np.clip(np.arctan2(u[1], u[0]), 0, np.pi / 2))
def sample(self):
return np.random.uniform(low=self.lower_bound(), high=self.upper_bound())
def lower_bound(self):
return ndarray([.01, .01, .59, .01, .01])
def upper_bound(self):
return ndarray([.39, .59, .99, .99, .59])
|