def reaction() -> None:
"""A simple exponential reaction model on a 1D grid.
"""
instance = Instance({
Operator.F_INIT: ['initial_state'], # list of float
Operator.O_F: ['final_state']}) # list of float
while instance.reuse_instance():
# F_INIT
t_max = instance.get_setting('t_max', 'float')
dt = instance.get_setting('dt', 'float')
k = instance.get_setting('k', 'float')
msg = instance.receive('initial_state')
U = np.array(msg.data)
t_cur = msg.timestamp
while t_cur + dt < t_max:
# O_I
# S
U += k * U * dt
t_cur += dt
# O_F
instance.send('final_state', Message(t_cur, None, U.tolist()))
def explicit_relay():
"""Intermediate component with explicit settings.
Sends and receives overlay settings explicitly, rather than
having MUSCLE handle them. This just passes all information on.
"""
instance = Instance({
Operator.F_INIT: ['in[]'], Operator.O_F: ['out[]']})
while instance.reuse_instance(False):
# f_init
assert instance.get_setting('test2', 'float') == 13.3
assert instance.get_port_length('in') == instance.get_port_length(
'out')
msgs = list()
for slot in range(instance.get_port_length('in')):
msg = instance.receive_with_settings('in', slot)
assert msg.data.startswith('testing')
assert msg.settings['test2'] == 14.4
msgs.append(msg)
assert instance.get_setting('test2') == 13.3
# o_f
for slot in range(instance.get_port_length('out')):
instance.send('out', msgs[slot], slot)
def diffusion() -> None:
"""A simple diffusion model on a 1d grid.
The state of this model is a 1D grid of concentrations. It sends
out the state on each timestep on `state_out`, and can receive an
updated state on `state_in` at each state update.
"""
logger = logging.getLogger()
instance = Instance({
Operator.O_I: ['state_out'],
Operator.S: ['state_in']
})
while instance.reuse_instance():
# F_INIT
t_max = instance.get_setting('t_max', 'float')
dt = instance.get_setting('dt', 'float')
x_max = instance.get_setting('x_max', 'float')
dx = instance.get_setting('dx', 'float')
d = instance.get_setting('d', 'float')
U = np.zeros(int(round(x_max / dx)))
U[25] = 2.0
U[50] = 2.0
U[75] = 2.0
Us = U
t_cur = 0.0
while t_cur + dt <= t_max:
# O_I
t_next = t_cur + dt
if t_next + dt > t_max:
t_next = None
cur_state_msg = Message(t_cur, t_next, U.tolist())
instance.send('state_out', cur_state_msg)
# S
msg = instance.receive('state_in', default=cur_state_msg)
if msg.timestamp > t_cur + dt:
logger.warning('Received a message from the future!')
U = np.array(msg.data)
dU = np.zeros_like(U)
dU[1:-1] = d * laplacian(U, dx) * dt
dU[0] = dU[1]
dU[-1] = dU[-2]
U += dU
Us = np.vstack((Us, U))
t_cur += dt
plt.figure()
plt.imshow(np.log(Us + 1e-20))
plt.show()
def macro():
instance = Instance({
Operator.O_I: ['out'],
Operator.S: ['in']})
while instance.reuse_instance():
# f_init
assert instance.get_setting('test1') == 13
for i in range(2):
# o_i
test_array = np.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])
assert test_array.shape == (2, 3)
assert test_array.flags.c_contiguous
data = {
'message': 'testing',
'test_grid': test_array}
instance.send('out', Message(i * 10.0, (i + 1) * 10.0, data))
# s/b
msg = instance.receive('in')
assert msg.data['reply'] == 'testing back {}'.format(i)
assert msg.data['test_grid'].array.dtype.kind == 'i'
assert msg.data['test_grid'].array.dtype.itemsize == 8
assert msg.data['test_grid'].array[0][1] == 2
assert msg.timestamp == i * 10.0
def micro():
"""Micro model implementation.
"""
instance = Instance({Operator.F_INIT: ['in'], Operator.O_F: ['out']})
while instance.reuse_instance():
# f_init
assert instance.get_setting('test3', 'str') == 'testing'
assert instance.get_setting('test4', 'bool') is True
assert instance.get_setting('test6', '[[float]]')[0][1] == 2.0
msg = instance.receive('in')
assert msg.data == 'testing'
# o_f
instance.send('out', Message(0.1, None, 'testing back'))
def micro():
"""Micro model implementation.
"""
instance = Instance({Operator.F_INIT: ['in'], Operator.O_F: ['out']})
assert instance.get_setting('test2') == 13.3
while instance.reuse_instance():
# f_init
assert instance.get_setting('test2', 'float') == 14.4
msg = instance.receive('in')
assert msg.data == 'testing'
# with pytest.raises(RuntimeError):
# instance.receive_with_settings('in')
# o_f
instance.send('out', Message(0.1, None, 'testing back'))
def micro():
"""Micro model implementation.
"""
instance = Instance({Operator.F_INIT: ['in'], Operator.O_F: ['out']})
while instance.reuse_instance():
# f_init
assert instance.get_setting('test3', 'str') == 'testing'
assert instance.get_setting('test4', 'bool') is True
assert instance.get_setting('test6', '[[float]]')[0][1] == 2.0
msg = instance.receive('in')
assert msg.data == 'testing'
# o_f
result = {
'string': 'testing back',
'int': 42,
'float': 3.1416,
'grid': Grid(np.array([[12.0, 34.0, 56.0], [1.0, 2.0, 3.0]]))
}
instance.send('out', Message(0.1, None, result))
def macro():
"""Macro model implementation.
"""
instance = Instance({
Operator.O_I: ['out'], Operator.S: ['in']})
while instance.reuse_instance():
# f_init
assert instance.get_setting('test2') == 14.4
# o_i
instance.send('out', Message(0.0, 10.0, 'testing'))
# s/b
msg = instance.receive('in')
assert msg.data == 'testing back'
def macro():
instance = Instance({Operator.O_I: ['out'], Operator.S: ['in']})
while instance.reuse_instance():
# f_init
assert instance.get_setting('test1') == 13
for i in range(2):
# o_i
instance.send('out', Message(i * 10.0, (i + 1) * 10.0, 'testing'))
# s/b
msg = instance.receive('in')
assert msg.data == 'testing back {}'.format(i)
assert msg.timestamp == i * 10.0
def macro():
"""Macro model implementation.
"""
instance = Instance({Operator.O_I: ['out[]'], Operator.S: ['in[]']})
while instance.reuse_instance():
# f_init
assert instance.get_setting('test1') == 13
# o_i
assert instance.is_vector_port('out')
for slot in range(10):
instance.send('out', Message(0.0, 10.0, 'testing'), slot)
# s/b
for slot in range(10):
msg = instance.receive('in', slot)
assert msg.data == 'testing back'
def macro():
"""Macro model implementation.
"""
instance = Instance({Operator.O_I: ['out[]'], Operator.S: ['in[]']})
while instance.reuse_instance():
# f_init
assert instance.get_setting('test1') == 13
# o_i
assert instance.is_vector_port('out')
for slot in range(10):
instance.send('out', Message(0.0, 10.0, 'testing'), slot)
# s/b
for slot in range(10):
msg = instance.receive('in', slot)
assert msg.data['string'] == 'testing back'
assert msg.data['int'] == 42
assert msg.data['float'] == 3.1416
assert msg.data['grid'].array.dtype == np.float64
assert msg.data['grid'].array[0, 1] == 34.0
def gray_scott_macro():
#######################
# MUSCLE modification #
#######################
# define the MUSCLE in and out ports
instance = Instance({Operator.O_I: ['state_out'], Operator.S: ['sgs_in']})
while instance.reuse_instance():
# Main script
# gray scott parameters
feed = instance.get_setting('feed')
kill = instance.get_setting('kill')
HOME = os.path.abspath(os.path.dirname(__file__))
###########################
# End MUSCLE modification #
###########################
# number of gridpoints in 1D
I = 7
N = 2**I
N_ref = 2**(I + 1)
# number of time series to track
N_Q = 2
# domain size [-L, L]
L = 1.25
# user flags
store = True
state_store = True
restart = False
sim_ID = 'test_gray_scott'
# TRAINING DATA SET
QoI = ['Q_HF', 'Q_ref']
Q = len(QoI)
# allocate memory
samples = {}
if store:
samples['N'] = N
for q in range(Q):
samples[QoI[q]] = []
# 2D grid, scaled by L
xx, yy = get_grid(N, L)
xx_ref, yy_ref = get_grid(N_ref, L)
# spatial derivative operators
kx, ky = get_derivative_operator(N, L)
kx_ref, ky_ref = get_derivative_operator(N_ref, L)
# Laplace operator
k_squared = kx**2 + ky**2
k_squared_ref = kx_ref**2 + ky_ref**2
# diffusion coefficients
epsilon_u = 2e-5
epsilon_v = 1e-5
# time step parameters
dt = 0.5
n_steps = int(5000 / dt)
store_frame_rate = 1
t = 0.0
# Initial condition
if restart:
fname = HOME + '/restart/' + sim_ID + '_t_' + str(np.around(
t, 1)) + '.hdf5'
# if fname does not exist, select restart file via GUI
if os.path.exists(fname) == False:
root = tk.Tk()
root.withdraw()
fname = filedialog.askopenfilename(
initialdir=HOME + '/restart',
title="Open restart file",
filetypes=(('HDF5 files', '*.hdf5'), ('All files', '*.*')))
# create HDF5 file
h5f = h5py.File(fname, 'r')
for key in h5f.keys():
print(key)
vars()[key] = h5f[key][:]
h5f.close()
else:
u_hat, v_hat = initial_cond(xx, yy)
u_hat_ref, v_hat_ref = initial_cond(xx_ref, yy_ref)
# Integrating factors
int_fac_u, int_fac_u2, int_fac_v, int_fac_v2 = \
integrating_factors(k_squared, dt, epsilon_u, epsilon_v)
int_fac_u_ref, int_fac_u2_ref, int_fac_v_ref, int_fac_v2_ref = \
integrating_factors(k_squared_ref, dt, epsilon_u, epsilon_v)
# counters
j = 0
j2 = 0
V_hat_1 = np.fft.fft2(np.ones([N, N]))
V_hat_1_ref = np.fft.fft2(np.ones([N_ref, N_ref]))
t0 = time.time()
samples_uq = np.zeros([n_steps, 8])
# time stepping
for n in range(n_steps):
u_hat_ref, v_hat_ref = rk4(u_hat_ref, v_hat_ref, int_fac_u_ref,
int_fac_u2_ref, int_fac_v_ref,
int_fac_v2_ref, dt, feed, kill)
# compute reference stats
Q_HF = np.zeros(2 * N_Q)
Q_HF[0] = compute_int(V_hat_1, u_hat, N)
Q_HF[1] = 0.5 * compute_int(u_hat, u_hat, N)
Q_HF[2] = compute_int(V_hat_1, v_hat, N)
Q_HF[3] = 0.5 * compute_int(v_hat, v_hat, N)
Q_ref = np.zeros(2 * N_Q)
Q_ref[0] = compute_int(V_hat_1_ref, u_hat_ref, N_ref)
Q_ref[1] = 0.5 * compute_int(u_hat_ref, u_hat_ref, N_ref)
Q_ref[2] = compute_int(V_hat_1_ref, v_hat_ref, N_ref)
Q_ref[3] = 0.5 * compute_int(v_hat_ref, v_hat_ref, N_ref)
samples_uq[n, 0:2 * N_Q] = Q_HF
samples_uq[n, 2 * N_Q:] = Q_ref
if np.mod(n, 100) == 0:
print('time step %d of %d' % (n, n_steps))
print(Q_HF)
print(Q_ref)
#######################
# MUSCLE modification #
#######################
# MUSCLE O_I port (state_out)
t_cur = n * dt
t_next = t_cur + dt
if n == n_steps - 1:
t_next = None
# split state vars in real and imag part (temporary fix)
V_hat_1_re = np.copy(V_hat_1.real)
V_hat_1_im = np.copy(V_hat_1.imag)
u_hat_re = np.copy(u_hat.real)
u_hat_im = np.copy(u_hat.imag)
v_hat_re = np.copy(v_hat.real)
v_hat_im = np.copy(v_hat.imag)
# create a MUSCLE Message object, to be sent to the micro model
cur_state = Message(
t_cur, t_next, {
'V_hat_1_re': V_hat_1_re,
'V_hat_1_im': V_hat_1_im,
'u_hat_re': u_hat_re,
'u_hat_im': u_hat_im,
'v_hat_re': v_hat_re,
'v_hat_im': v_hat_im,
'Q_ref': Q_ref,
'Q_model': Q_HF
})
# send the message to the micro model
instance.send('state_out', cur_state)
# reveive a message from the micro model, i.e. the two reduced subgrid-scale terms
msg = instance.receive('sgs_in')
reduced_sgs_u_re = msg.data['reduced_sgs_u_re'].array
reduced_sgs_u_im = msg.data['reduced_sgs_u_im'].array
reduced_sgs_v_re = msg.data['reduced_sgs_v_re'].array
reduced_sgs_v_im = msg.data['reduced_sgs_v_im'].array
# recreate the reduced subgrid-scale terms for the u and v pde
reduced_sgs_u = reduced_sgs_u_re + 1.0j * reduced_sgs_u_im
reduced_sgs_v = reduced_sgs_v_re + 1.0j * reduced_sgs_v_im
###########################
# End MUSCLE modification #
###########################
if np.mod(n, 1000) == 0:
print('time step %d of %d' % (n, n_steps))
# evolve the state in time, with the new reduced sgs terms
u_hat, v_hat = rk4(u_hat,
v_hat,
int_fac_u,
int_fac_u2,
int_fac_v,
int_fac_v2,
dt,
feed,
kill,
reduced_sgs_u=reduced_sgs_u,
reduced_sgs_v=reduced_sgs_v)
j += 1
j2 += 1
t += dt
if j2 == store_frame_rate and store:
j2 = 0
for qoi in QoI:
samples[qoi].append(eval(qoi))
# foo = False
t1 = time.time()
print('*************************************')
print('Simulation time = %f [s]' % (t1 - t0))
print('*************************************')
# output csv file
header = 'Q1,Q2,Q3,Q4,Q1_HF,Q2_HF,Q3_HF,Q4_HF'
fname = 'output_f%.5f_k%.5f.csv' % (feed, kill)
np.savetxt(fname, samples_uq, delimiter=",", comments='', header=header)
# store the state of the system to allow for a simulation restart at t > 0
if state_store:
keys = ['u_hat', 'v_hat']
if os.path.exists(HOME + '/restart') == False:
os.makedirs(HOME + '/restart')
fname = HOME + '/restart/' + sim_ID + '_t_' + str(np.around(
t, 1)) + '.hdf5'
# create HDF5 file
h5f = h5py.File(fname, 'w')
# store numpy sample arrays as individual datasets in the hdf5 file
for key in keys:
qoi = eval(key)
h5f.create_dataset(key, data=qoi)
h5f.close()
def diffusion() -> None:
"""A simple diffusion model on a 1d grid.
The state of this model is a 1D grid of concentrations. It sends
out the state on each timestep on `state_out`, and can receive an
updated state on `state_in` at each state update.
"""
logger = logging.getLogger()
instance = Instance({
Operator.O_I: ['state_out'],
Operator.S: ['state_in']
})
while instance.reuse_instance():
# F_INIT
t_max = instance.get_setting('t_max', 'float')
dt = instance.get_setting('dt', 'float')
x_max = instance.get_setting('x_max', 'float')
dx = instance.get_setting('dx', 'float')
d = instance.get_setting('d', 'float')
U = np.zeros(int(round(x_max / dx))) + 1e-20
U[25] = 2.0
U[50] = 2.0
U[75] = 2.0
Us = U
t_cur = 0.0
while t_cur + dt <= t_max:
# O_I
t_next = t_cur + dt
if t_next + dt > t_max:
t_next = None
cur_state_msg = Message(t_cur, t_next, Grid(U, ['x']))
instance.send('state_out', cur_state_msg)
# S
msg = instance.receive('state_in', default=cur_state_msg)
if msg.timestamp > t_cur + dt:
logger.warning('Received a message from the future!')
np.copyto(U, msg.data.array)
dU = np.zeros_like(U)
dU[1:-1] = d * laplacian(U, dx) * dt
dU[0] = dU[1]
dU[-1] = dU[-2]
U += dU
Us = np.vstack((Us, U))
t_cur += dt
if 'DONTPLOT' not in os.environ:
from matplotlib import pyplot as plt
plt.figure()
plt.imshow(np.log(Us + 1e-20),
origin='upper',
extent=[
-0.5 * dx, x_max - 0.5 * dx,
(t_max - 0.5 * dt) * 1000.0, -0.5 * dt * 1000.0
],
interpolation='none',
aspect='auto')
cbar = plt.colorbar()
cbar.set_label('log(Concentration)', rotation=270, labelpad=20)
plt.xlabel('x')
plt.ylabel('t (ms)')
plt.title('Concentration over time')
plt.show()
def qmc_driver() -> None:
"""A driver for quasi-Monte Carlo Uncertainty Quantification.
This component attaches to a collection of model instances, and
feeds in different parameter values generated using a Sobol
sequence.
"""
instance = Instance({
Operator.O_I: ['parameters_out[]'],
Operator.S: ['states_in[]']})
while instance.reuse_instance():
# F_INIT
# get and check parameter distributions
n_samples = instance.get_setting('n_samples', 'int')
d_min = instance.get_setting('d_min', 'float')
d_max = instance.get_setting('d_max', 'float')
k_min = instance.get_setting('k_min', 'float')
k_max = instance.get_setting('k_max', 'float')
if d_max < d_min:
instance.error_shutdown('Invalid settings: d_max < d_min')
exit(1)
if k_max < k_min:
instance.error_shutdown('Invalid settings: k_max < k_min')
exit(1)
# generate UQ parameter values
sobol_sqn = sobol_seq.i4_sobol_generate(2, n_samples)
ds = d_min + sobol_sqn[:, 0] * (d_max - d_min)
ks = k_min + sobol_sqn[:, 1] * (k_max - k_min)
# configure output port
if not instance.is_resizable('parameters_out'):
instance.error_shutdown('This component needs a resizable'
' parameters_out port, but it is connected to'
' something that cannot be resized. Maybe try'
' adding a load balancer.')
exit(1)
instance.set_port_length('parameters_out', n_samples)
# run ensemble
Us = None
# O_I
for sample in range(n_samples):
uq_parameters = Settings({
'd': ds[sample],
'k': ks[sample]})
msg = Message(0.0, None, uq_parameters)
instance.send('parameters_out', msg, sample)
# S
for sample in range(n_samples):
msg = instance.receive_with_settings('states_in', sample)
U = np.array(msg.data)
# accumulate
if Us is None:
Us = U
else:
Us = np.vstack((Us, U))
mean = np.mean(Us, axis=0)
# O_F
if 'DONTPLOT' not in os.environ:
from matplotlib import pyplot as plt
t_max = instance.get_setting('t_max', 'float')
dt = instance.get_setting('dt', 'float')
x_max = instance.get_setting('x_max', 'float')
dx = instance.get_setting('dx', 'float')
plt.figure()
plt.imshow(
np.log(Us + 1e-20),
origin='upper',
extent=[
-0.5*dx, x_max - 0.5*dx,
n_samples-0.5, -0.5],
interpolation='none',
aspect='auto'
)
cbar = plt.colorbar()
cbar.set_label('log(Concentration)', rotation=270, labelpad=20)
plt.xlabel('x')
plt.ylabel('Sample')
plt.title('Final states')
plt.show()
def qmc_driver() -> None:
"""A driver for quasi-Monte Carlo Uncertainty Quantification.
This component attaches to a collection of model instances, and
feeds in different parameter values generated using a Sobol
sequence.
"""
instance = Instance({
Operator.O_I: ['parameters_out[]'],
Operator.S: ['states_in[]']
})
while instance.reuse_instance():
# F_INIT
# get and check parameter distributions
n_samples = instance.get_setting('n_samples', 'int')
d_min = instance.get_setting('d_min', 'float')
d_max = instance.get_setting('d_max', 'float')
k_min = instance.get_setting('k_min', 'float')
k_max = instance.get_setting('k_max', 'float')
if d_max < d_min:
instance.error_shutdown('Invalid settings: d_max < d_min')
exit(1)
if k_max < k_min:
instance.error_shutdown('Invalid settings: k_max < k_min')
exit(1)
# generate UQ parameter values
sobol_sqn = sobol_seq.i4_sobol_generate(2, n_samples)
ds = d_min + sobol_sqn[:, 0] * (d_max - d_min)
ks = k_min + sobol_sqn[:, 1] * (k_max - k_min)
# configure output port
if not instance.is_resizable('parameters_out'):
instance.error_shutdown(
'This component needs a resizable'
' parameters_out port, but it is connected to'
' something that cannot be resized. Maybe try'
' adding a load balancer.')
exit(1)
instance.set_port_length('parameters_out', n_samples)
# run ensemble
Us = None
# O_I
for sample in range(n_samples):
uq_parameters = Settings({'d': ds[sample], 'k': ks[sample]})
msg = Message(0.0, None, uq_parameters)
instance.send('parameters_out', msg, sample)
# S
for sample in range(n_samples):
msg = instance.receive_with_settings('states_in', sample)
U = np.array(msg.data)
# accumulate
if Us is None:
Us = U
else:
Us = np.vstack((Us, U))
mean = np.mean(Us, axis=0)
plt.figure()
plt.imshow(np.log(Us + 1e-20))
plt.show()
def reduced_sgs():
"""
An EasySurrogate Reduced micro model, executed in a separate file and linked to the
macro model via MUSCLE3
"""
instance = Instance({
Operator.F_INIT: ['state_in'], # a dict with state values
Operator.O_F: ['sgs_out']
}) # a dict with subgrid-scale terms
# get some parameters
N_Q = instance.get_setting('N_Q') # the number of QoI to track, per PDE
N_LF = instance.get_setting(
'N_LF') # the number of gridpoints in 1 dimension
# t_max = instance.get_setting('t_max') #the simulation time, per time-step of macro
# dt = instance.get_setting('dt') #the micro time step
logger = logging.getLogger()
logger.setLevel(logging.DEBUG)
# Create an EasySurrogate RecucedSurrogate object
surrogate = es.methods.Reduced_Surrogate(N_Q, N_LF)
while instance.reuse_instance():
# receive the state from the macro model
msg = instance.receive('state_in')
V_hat_1_re = msg.data['V_hat_1_re'].array.T
V_hat_1_im = msg.data['V_hat_1_im'].array.T
u_hat_re = msg.data['u_hat_re'].array.T
u_hat_im = msg.data['u_hat_im'].array.T
v_hat_re = msg.data['v_hat_re'].array.T
v_hat_im = msg.data['v_hat_im'].array.T
Q_ref = msg.data['Q_ref'].array.T
Q_model = msg.data['Q_model'].array.T
# recreate the Fourier coefficients (temporary fix)
V_hat_1 = V_hat_1_re + 1.0j * V_hat_1_im
u_hat = u_hat_re + 1.0j * u_hat_im
v_hat = v_hat_re + 1.0j * v_hat_im
# #time of the macro model
t_cur = msg.timestamp
# train the two reduced sgs source terms using the recieved reference data Q_ref
reduced_dict_u = surrogate.train([V_hat_1, u_hat],
Q_ref[0:N_Q] - Q_model[0:N_Q])
reduced_dict_v = surrogate.train([V_hat_1, v_hat],
Q_ref[N_Q:] - Q_model[N_Q:])
# get the two reduced sgs terms from the dict
reduced_sgs_u = np.fft.ifft2(reduced_dict_u['sgs_hat'])
reduced_sgs_v = np.fft.ifft2(reduced_dict_v['sgs_hat'])
# MUSCLE O_F port (sgs), send the subgrid-scale terms back to the macro model
reduced_sgs_u_re = np.copy(reduced_sgs_u.real)
reduced_sgs_u_im = np.copy(reduced_sgs_u.imag)
reduced_sgs_v_re = np.copy(reduced_sgs_v.real)
reduced_sgs_v_im = np.copy(reduced_sgs_v.imag)
instance.send(
'sgs_out',
Message(
t_cur, None, {
'reduced_sgs_u_re': reduced_sgs_u_re,
'reduced_sgs_u_im': reduced_sgs_u_im,
'reduced_sgs_v_re': reduced_sgs_v_re,
'reduced_sgs_v_im': reduced_sgs_v_im
}))
