def knn_classify(data_file, K=5):
# f_train, f_test, l_train, l_test = get_data(data_file)
f_train, f_test, l_train, l_test = get_data_optimized(data_file)
l_predict = []
for t in range(f_test.shape[0]):
N = []
l = 0
for d in range(f_train.shape[0]):
if len(N) <= K:
N.append(d)
else:
for u in N:
if dist(f_test[t], f_train[d]) < dist(f_test[t], f_train[u]):
N.remove(u)
N.append(d)
break
for n in N:
if l_train[n] == 'A':
l += 1
else:
l -= 1
if l >= 0:
l_predict.append('A')
else:
l_predict.append('B')
acc = (float(sum(l_predict == l_test))/len(l_predict))
plot(f_train, l_train, f_test, l_test, l_predict, acc)
def create_histogram(dimensions, label):
numberofvalues = len(dimensions)
#calculates the width for each annotation across the labels
width = [width for width, height in dimensions.values()] #95 percent
width_zoom = sorted([width for width, height in dimensions.values()
])[:int(.95 * numberofvalues)]
#calculates height of each annotations across the labels
height = [height for width, height in dimensions.values()] #95 percent
height_zoom = sorted([height for width, height in dimensions.values()
])[:int(.95 * numberofvalues)]
#calculates aspect ratio of each annotation across the labels
aspect_ratio = [width / height for width, height in dimensions.values()]
aspect_ratio_zoom = sorted([
width / height for width, height in dimensions.values()
])[:int(.95 * numberofvalues)]
# calculates areas of each annotation across the labels
areas = [(width * height) / 100 for width, height in dimensions.values()]
areas_zoom = sorted([
(width * height) / 100 for width, height in dimensions.values()
])[:int(.85 * numberofvalues)]
#bins = np.arange(start=min(areas),stop=300,step=30)
# plot(width,label,'Width')
# plot(height,label,'Height')
# plot(aspect_ratio,label,'Aspect Ratio')
plot(areas_zoom, label, 'Areas Zoom')
def constantFrequencyExample(start=1.9, duration=0.5):
filteredSignal = helpers.getSignal(start, duration, low_pass=100, high_pass=90, input_file="raw-epdf.wav")
spectrum = helpers.getSpectrum(start, duration, low_pass=100, high_pass=90, input_file="raw-epdf.wav")
segment = helpers.getSegment(start, duration, input_file="raw-epdf.wav")
helpers.makeWavFromSpectrum(spectrum, segment, outputFile="recoveredWav.wav")
# firstPeak = min([i[0] for i in spectrum.peaks()])
helpers.plot(spectrum)
def generate_borders(source,
borders_only=False,
labels=False,
self_clip=False,
trim_antarctica=False):
"""data from http://www.naturalearthdata.com/"""
sf = shapefile.Reader("data/{}_admin_0_countries".format(source))
sovereigns = {} #key is 3-char code, value is list of (record,shape)
for record, shape in zip(sf.records(), sf.shapes()):
if trim_antarctica:
if record[4] == 'ATA': #if it is Antarctica
shape.points = trim_edges(shape.points)
sovereigns[record[4]] = sovereigns.get(record[4],
[]) + [(record, shape)]
for code in sorted(sovereigns.keys()):
for record, shape in sovereigns[code]:
if record[3] == record[8]:
country_code = record[12]
# metropole = (record, shape)
# sovereigns[code].remove(metropole) #move the metropole to the front
# sovereigns[code] = [metropole] + sovereigns[code]
# break
print('\t\t\t<g id="{}">'.format(country_code))
for record, shape in sovereigns[code]:
x1, y1, x2, y2 = shape.bbox
x = (x1 + x2) / 2
y = (y1 + y2) / 2
region_code = record[12]
if country_code == region_code: #metropole
# name = record[3]
text_size = SIZE_CLASSES[int(record[2] - 2)]
else: #dependency
# name = '{} ({})'.format(record[8], record[3])
text_size = SIZE_CLASSES[int(record[2] - 1)]
# if labels:
# if text_size is not None:
# print('\t\t\t\t<text class="label-{}" x="{:.3f}" y="{:.3f}">{}</text>'.format(text_size, x, y, name))
if borders_only:
print(
'\t\t\t\t<clipPath id="{0}-clipPath">'.format(region_code))
print(
'\t\t\t\t\t<use href="#{0}-shape" />'.format(region_code))
print('\t\t\t\t</clipPath>')
print(
'\t\t\t\t<use href="#{0}-shape" style="fill:none; clip-path:url(#{0}-clipPath);" />'
.format(region_code))
else:
plot(shape.points,
midx=shape.parts,
close=False,
fourmat='xd',
tabs=4,
ident="{0}-shape".format(region_code))
print('\t\t\t</g>')
def harmonics(base_frequency=400):
# cos_sig = thinkdsp.CosSignal(freq=440, amp=1.0, offset=0)
base_signal = thinkdsp.CosSignal(base_frequency, amp=1.0, offset=0)
for i in xrange(2, 6):
base_signal += thinkdsp.CosSignal(base_frequency * i, amp=1.0, offset=0)
wave = base_signal.make_wave(duration=0.5, start=0, framerate=11025)
spectrum = wave.make_spectrum()
# helpers.makeWavFromSpectrum(spectrum, wave, 'exercise7.wav')
helpers.plot(spectrum)
def underWaterSpectrum(signal, distance, absorbtionRate): spectrum = signal.make_spectrum() originalSpectrum = signal.make_spectrum() baseFrequency = getBaseFrequency(signal) index = 0; for freq in spectrum.fs: attenuation = attenuationFactor(distance, absorbtionRate, baseFrequency, freq) spectrum.amps[index] = spectrum.amps[index]/attenuation index += 1 helpers.plot(spectrum) return spectrum
def plot_side_indicatrix(phi0, r, res, side_res=1):
points = []
midx = [0]
for l in range(0, 181, 360 // res):
pr, lr = obliquify(math.pi / 2 - r, math.radians(l), phi0, 0)
points.append((pr, lr - math.pi))
for i in range(side_res):
points.append((phi0 + r - (2 * r) / side_res * (i + 1), -math.pi))
midx.append(len(points))
for l in range(180, 361, 360 // res):
pr, lr = obliquify(math.pi / 2 - r, math.radians(l), phi0, 0)
points.append((pr, lr + math.pi))
for i in range(side_res):
points.append((phi0 - r + (2 * r) / side_res * (i + 1), math.pi))
plot(points, midx=midx, close=False)
def create_plot(doc):
"""Create a static plot."""
doc.clear()
# doc.theme = Theme(filename=join(getcwd(), 'theme.yaml'))
sp = StockPrices()
figure = plot(5, PLOT_WIDTH, PLOT_HEIGHT, get_data(sp, SELECTED, 5))
doc.add_root(figure)
def plot_shape(data,
source,
max_rank,
trim_antarctica=False,
flesh_out_antarctica=False):
"""data from http://www.naturalearthdata.com/"""
sf = shapefile.Reader("data/{}_{}".format(source, data))
for i, field in enumerate(sf.fields):
if 'rank' in field[0]:
rank_idx = i - 1
for record, shape in zip(sf.records(), sf.shapes()):
if record[rank_idx] <= max_rank:
if trim_antarctica:
if shape.points[0][
1] < -60: #if it is Antarctica (this will have a few false positives, but that's fine)
shape.points = trim_edges(shape.points)
elif flesh_out_antarctica:
if shape.points[0][1] < -60:
shape.points = lengthen_edges(shape.points)
plot(shape.points, midx=shape.parts, close=False, fourmat='xd')
def update_period(attr, old, new):
"""Update selected period."""
spinner.css_classes = ['loader-spinner']
overlay.css_classes = ['loader-overlay']
_data = get_data(sp, selected, period_selector.active)
layout.children[2] = plot(period_selector.active, plot_width,
plot_height, _data)
spinner.css_classes = []
overlay.css_classes = []
def plot_pole_indicatrix(north,
r,
res,
ctr_meridian=0,
side_res=1,
pole_res=1):
if north:
pp, pr = math.pi / 2, math.pi / 2 - r
else:
pp, pr = -math.pi / 2, -math.pi / 2 + r
points = []
for i in range(side_res):
points.append((pp + (pr - pp) / side_res * i, ctr_meridian - math.pi))
for x in range(-180, 181, 360 // res):
points.append((pr, ctr_meridian + math.radians(x)))
for i in range(side_res):
points.append(
(pr + (pp - pr) / side_res * (i + 1), ctr_meridian + math.pi))
for x in range(180, -181, -360 // pole_res):
points.append((pp, ctr_meridian + math.radians(x)))
plot(points)
def update_symbol_list(attr, old, new):
"""Update selected symobls."""
spinner.css_classes = ['loader-spinner']
overlay.css_classes = ['loader-overlay']
if symbol_selector.value is None:
return
if symbol_selector.value in selected:
selected.remove(symbol_selector.value)
else:
selected.append(symbol_selector.value)
if selected is None:
_data = None
else:
_data = get_data(sp, selected, period_selector.active)
layout.children[2] = plot(period_selector.active, plot_width,
plot_height, _data)
symbol_selector.value = None
spinner.css_classes = []
overlay.css_classes = []
def test():
with pygmsh.occ.Geometry() as geom:
container = geom.add_rectangle([0.0, 0.0, 0.0], 10.0, 10.0)
letter_i = geom.add_rectangle([2.0, 2.0, 0.0], 1.0, 4.5)
i_dot = geom.add_disk([2.5, 7.5, 0.0], 0.6)
disk1 = geom.add_disk([6.25, 4.5, 0.0], 2.5)
disk2 = geom.add_disk([6.25, 4.5, 0.0], 1.5)
letter_o = geom.boolean_difference(disk1, disk2)
geom.boolean_difference(
container, geom.boolean_union([letter_i, i_dot, letter_o]))
mesh = geom.generate_mesh()
ref = 81.9131851877
assert abs(compute_volume(mesh) - ref) < 1.0e-2 * ref
return mesh
if __name__ == "__main__":
# import meshio
# meshio.write_points_cells('m.vtu', *test())
from helpers import plot
mesh = test()
plot("meshio_logo.png", mesh.points, mesh.get_cells_type("triangle"))
rect3 = geom.add_rectangle([10.0, 30.0, 0.0], 10.0, 1.0)
rect4 = geom.add_rectangle([20.0, 9.0, 0.0], 10.0, 1.0)
r1 = geom.add_rectangle([9.0, 0.0, 0.0], 21.0, 20.5, corner_radius=8.0)
r2 = geom.add_rectangle([10.0, 00.0, 0.0], 20.0, 19.5, corner_radius=7.0)
diff1 = geom.boolean_difference([r1], [r2])
r22 = geom.add_rectangle([9.0, 10.0, 0.0], 11.0, 11.0)
inter1 = geom.boolean_intersection([diff1, r22])
r3 = geom.add_rectangle([10.0, 19.5, 0.0], 21.0, 21.0, corner_radius=8.0)
r4 = geom.add_rectangle([10.0, 20.5, 0.0], 20.0, 20.0, corner_radius=7.0)
diff2 = geom.boolean_difference([r3], [r4])
r33 = geom.add_rectangle([20.0, 19.0, 0.0], 11.0, 11.0)
inter2 = geom.boolean_intersection([diff2, r33])
geom.boolean_difference([rect1, rect2],
[disk1, disk2, rect3, rect4, inter1, inter2])
points, cells, _, _, _ = pygmsh.generate_mesh(geom)
ref = 1082.4470502181903
assert abs(compute_volume(points, cells) - ref) < 1.0e-2 * ref
return points, cells
if __name__ == '__main__':
from helpers import plot
plot('logo.png', *test())
# import meshio
# meshio.write('logo.vtu', *test())
import copy from elliptic_curve import EllipticCurve from helpers import plot from point import Point C = EllipticCurve(a=-2, b=4) print(C) # case where P + Q + r = 0 ( tree points on curve) P = Point(C, 3, 5) P_copy = copy.copy(P) Q = Point(C, -2, 0) U = P+Q print(U) plot(C, P_copy, Q, U) # case where P + P + 0 = 0 (only one point on curve) P = Point(C, -2, 0) P_copy = copy.copy(P) Q = Point(C, -2, 0) U = P+Q print(U) plot(C, P_copy, Q, U) # case where P + Q + 0 = 0 (vertical line) P = Point(C, 0, 2) P_copy = copy.copy(P) Q = Point(C, 0, -2) U = P+Q print(U)
def main(): spectrum = getSquareWaveSignal(1100).make_wave().make_spectrum() helpers.plot(spectrum)
print(f"J={J}")
# L2 regularisation
#J += 1e4*reg
#print(f"reg={1e4*reg}")
# l2 regularisation
reg = 0
for W in [W_1, W_2, b_1, W_3_1, W_3_2, b_2]:
reg += 1e4*assemble(W**2*dx)
J += reg
print(f"reg={reg}")
Jhat = ReducedFunctional(J, [Control(W_1), Control(b_1), Control(W_2), Control(b_2), Control(W_3_1), Control(W_3_2)])
C_up_eps_1 = Control(up_eps_1)
C_up_eps_2 = Control(up_eps_2)
set_log_level(LogLevel.ERROR)
minimize(Jhat, tol=1e-200, options={"disp": True, "gtol": 1e-12, "maxiter": 20})
#print("|U - d| = ", assemble(inner(C_up.tape_value() - up_stab, C_up.tape_value() - up_stab)*dx)**0.5)
u_nn, p_nn = C_up_eps_1.tape_value().split(deepcopy=True)
plot(u_nn, "out/u_eps_1_nn.png")
plot(p_nn, "out/p_eps_1_nn.png")
u_nn, p_nn = C_up_eps_2.tape_value().split(deepcopy=True)
plot(u_nn, "out/u_eps_2_nn.png")
plot(p_nn, "out/p_eps_2_nn.png")
def train(u_stab, element):
mesh = u_stab.function_space().mesh()
n = FacetNormal(mesh)
W = FunctionSpace(mesh, element)
# Now solve the Poisson with an inconsistent element,
# but with the NN as a source term
# Define a neural network that will be added as a source term to the Poisson eqn
# We pass into the network the mesh size :_
R = VectorFunctionSpace(mesh, "R", 0, dim=50)
R2 = FunctionSpace(mesh, "R", 0)
W_1 = [Function(R)] * 5
W_2 = Function(R)
b_1 = Function(R)
b_2 = Function(R2)
eps = 1e1
for w in W_1:
w.vector()[:] = eps * rand(R.dim())
W_2.vector()[:] = eps * rand(R.dim())
b_1.vector()[:] = eps * rand(R.dim())
b_2.vector()[:] = eps * rand(R2.dim())
def nn(u, v):
inp = as_vector(
[avg(u), jump(u), *grad(avg(u)), *grad(jump(u)), *n('+')])
def sigma_(vec, func=ufl.tanh):
v = [func(vec[i]) for i in range(vec.ufl_shape[0])]
return ufl.as_vector(v)
relu = lambda vec: conditional(ufl.gt(vec, 0), vec, (ufl.exp(vec) - 1))
sigma = lambda vec: sigma_(vec, func=relu)
nn = dot(W_2, sigma(ufl.transpose(as_vector(W_1)) * inp + b_1)) + b_2
return inner(nn, jump(v) + avg(v)) * dS, inner(nn, nn) * dS
# Now solve the Stokes-NN forward problem
u, reg = poisson(W, nn)
plot(u, "out/u_nn0.png")
J = assemble((u - u_stab)**2 * dx)
print(f"J={J}")
# L2 regularisation
#J += 1e4*reg
#print(f"reg={1e4*reg}")
# l2 regularisation
reg = 0
for W in [*W_1, W_2, b_1, b_2]:
reg += 1e4 * assemble(W**2 * dx)
J += reg
print(f"reg={reg}")
ctrls = [Control(W) for W in W_1]
ctrls += [Control(b_1), Control(W_2), Control(b_2)]
Jhat = ReducedFunctional(J, ctrls)
C_u = Control(u)
set_log_level(LogLevel.ERROR)
minimize(Jhat,
tol=1e-200,
options={
"disp": True,
"gtol": 1e-12,
"maxiter": 20
})
print(
"|U - d| = ",
assemble(
inner(C_u.tape_value() - u_stab,
C_u.tape_value() - u_stab) * dx)**0.5)
u_nn = C_u.tape_value()
plot(u_nn, "out/u_nn.png")
return nn
#solve(F == 0, up, bcs, solver_parameters={"nonlinear_solver": "snes", "snes_solver": {"line_search": "bt", "linear_solver": "lu", "report": False}}, # [basic,bt,cp,l2,nleqerr]
# form_compiler_parameters={"optimize": True})
if nn:
return up, assemble(reg)
else:
return up
if __name__ == "__main__":
mesh = UnitSquareMesh(16, 16, 'crossed')
stable = [
VectorElement('Lagrange', triangle, 2),
FiniteElement('Lagrange', triangle, 1)
]
W = FunctionSpace(mesh, MixedElement(stable))
up = stokes(W)
# Add noise
eps_noise = 0
up.vector()[:] += eps_noise * rand(W.dim())
u_stab, p_stab = up.split(deepcopy=True)
plot(u_stab, "out/u_stab.png")
plot(p_stab, "out/p_stab.png")
with HDF5File(MPI.comm_world, "out/up_stab.h5", "w") as xdmf:
xdmf.write(up, "up")
def plot_indicatrix(phi0, lam0, r, res):
points = []
for l in range(0, 360, 360 // res):
points.append(obliquify(math.pi / 2 - r, math.radians(l), phi0, lam0))
plot(points)
def plot_orthodrome(phi0, lam0, tht0): points = [] for p in range(-90, 91): points.append(obliquify(math.radians(p), tht0, phi0, lam0)) plot(points, close=False)
def periodic_signal_spectrum(start=1.9, duration=4.8):
spectrum = helpers.getSpectrum(start, duration, low_pass=100, high_pass=90, input_file="raw-epdf.wav")
helpers.plot(spectrum)
def periodic_signal_example(start=1.9, duration=4.8): filteredSignal = helpers.getSignal(start, duration, low_pass=100, high_pass=90, input_file="raw-epdf.wav") helpers.plot(filteredSignal)
@pytest.mark.skipif(pygmsh.get_gmsh_major_version() < 3,
reason="requires Gmsh >= 3")
def test():
geom = pygmsh.opencascade.Geometry(characteristic_length_min=0.5,
characteristic_length_max=0.5)
container = geom.add_rectangle([0.0, 0.0, 0.0], 10.0, 10.0)
letter_i = geom.add_rectangle([2.0, 2.0, 0.0], 1.0, 4.5)
i_dot = geom.add_disk([2.5, 7.5, 0.0], 0.6)
disk1 = geom.add_disk([6.25, 4.5, 0.0], 2.5)
disk2 = geom.add_disk([6.25, 4.5, 0.0], 1.5)
letter_o = geom.boolean_difference([disk1], [disk2])
geom.boolean_difference([container], [letter_i, i_dot, letter_o])
mesh = pygmsh.generate_mesh(geom)
ref = 81.9131851877
assert abs(compute_volume(mesh) - ref) < 1.0e-2 * ref
return mesh
if __name__ == "__main__":
# import meshio
# meshio.write_points_cells('m.vtu', *test())
from helpers import plot
plot("meshio_logo.png", test())
def create_plot(doc):
"""Creat a bokeh plot."""
# create a plot and style its properties
# doc = curdoc()
doc.theme = Theme(filename=join(dirname(__file__), 'theme.yaml'))
doc.title = 'Sample bokeh plot'
sp = StockPrices()
plot_width = 600
plot_height = 600
# elements
symbol_selector = AutocompleteInput(completions=list(sp.get_symbols()),
width=150)
period_selector = RadioButtonGroup(labels=[
"Today" if datetime.today().weekday() < 5 else "Friday", "5 days",
"1 month", "6 months", "1 year", "5 years"
],
active=5,
width=400)
selected = ['GOOGL', 'AMZN']
spinner = Div(text='')
overlay = Div(text='')
layout = column(Div(text='<header><h1>Stock Closing Prices</h1></header>',
width=plot_width),
row(column(
widgetbox(Div(text='<h3>Period</h3>'),
period_selector,
width=400)),
column(
widgetbox(Div(text='<h3>Symbols</h3>'),
symbol_selector,
width=plot_width - 400)),
height=95),
plot(period_selector.active, plot_width, plot_height,
get_data(sp, selected, period_selector.active)),
spinner,
overlay,
width=plot_width + 20,
height=plot_height + 120,
sizing_mode='fixed')
# layout.css_classes = ['wrapper']
doc.add_root(layout)
# Set up callbacks
# symbol selector
def update_symbol_list(attr, old, new):
"""Update selected symobls."""
spinner.css_classes = ['loader-spinner']
overlay.css_classes = ['loader-overlay']
if symbol_selector.value is None:
return
if symbol_selector.value in selected:
selected.remove(symbol_selector.value)
else:
selected.append(symbol_selector.value)
if selected is None:
_data = None
else:
_data = get_data(sp, selected, period_selector.active)
layout.children[2] = plot(period_selector.active, plot_width,
plot_height, _data)
symbol_selector.value = None
spinner.css_classes = []
overlay.css_classes = []
symbol_selector.on_change('value', update_symbol_list)
# period selector
def update_period(attr, old, new):
"""Update selected period."""
spinner.css_classes = ['loader-spinner']
overlay.css_classes = ['loader-overlay']
_data = get_data(sp, selected, period_selector.active)
layout.children[2] = plot(period_selector.active, plot_width,
plot_height, _data)
spinner.css_classes = []
overlay.css_classes = []
period_selector.on_change('active', update_period)
if nn:
Fnn, reg = nn(u, v)
F += Fnn
solve(F == 0, u, bcs)
if nn:
return u, assemble(reg)
else:
return u
if __name__== "__main__":
mesh = UnitIntervalMesh(16)
stable = FiniteElement('Lagrange', interval, 1)
W = FunctionSpace(mesh, stable)
u = poisson(W)
# Add noise
eps_noise = 0
u.vector()[:] += eps_noise*rand(W.dim())
plot(u, "out/u_stab.png")
with HDF5File(MPI.comm_world, "out/u_stab.h5", "w") as xdmf:
xdmf.write(u, "u")
def main(): frequency = 10 for i in xrange(3): helpers.plot(removeHarmonics(sawToothSignal(freq=frequency), i)[1]) helpers.plot(getWave(sawToothSignal(freq=frequency)))
@pytest.mark.skipif(pygmsh.get_gmsh_major_version() < 3, reason="requires Gmsh >= 3")
def test():
geom = pygmsh.opencascade.Geometry(
characteristic_length_min=0.5, characteristic_length_max=0.5
)
container = geom.add_rectangle([0.0, 0.0, 0.0], 10.0, 10.0)
letter_i = geom.add_rectangle([2.0, 2.0, 0.0], 1.0, 4.5)
i_dot = geom.add_disk([2.5, 7.5, 0.0], 0.6)
disk1 = geom.add_disk([6.25, 4.5, 0.0], 2.5)
disk2 = geom.add_disk([6.25, 4.5, 0.0], 1.5)
letter_o = geom.boolean_difference([disk1], [disk2])
geom.boolean_difference([container], [letter_i, i_dot, letter_o])
mesh = pygmsh.generate_mesh(geom)
ref = 81.9131851877
assert abs(compute_volume(mesh) - ref) < 1.0e-2 * ref
return mesh
if __name__ == "__main__":
# import meshio
# meshio.write_points_cells('m.vtu', *test())
from helpers import plot
plot("meshio_logo.png", test())
rect3 = geom.add_rectangle([10.0, 30.0, 0.0], 10.0, 1.0)
rect4 = geom.add_rectangle([20.0, 9.0, 0.0], 10.0, 1.0)
r1 = geom.add_rectangle([9.0, 0.0, 0.0], 21.0, 20.5, corner_radius=8.0)
r2 = geom.add_rectangle([10.0, 00.0, 0.0], 20.0, 19.5, corner_radius=7.0)
diff1 = geom.boolean_difference([r1], [r2])
r22 = geom.add_rectangle([9.0, 10.0, 0.0], 11.0, 11.0)
inter1 = geom.boolean_intersection([diff1, r22])
r3 = geom.add_rectangle([10.0, 19.5, 0.0], 21.0, 21.0, corner_radius=8.0)
r4 = geom.add_rectangle([10.0, 20.5, 0.0], 20.0, 20.0, corner_radius=7.0)
diff2 = geom.boolean_difference([r3], [r4])
r33 = geom.add_rectangle([20.0, 19.0, 0.0], 11.0, 11.0)
inter2 = geom.boolean_intersection([diff2, r33])
geom.boolean_difference([rect1, rect2],
[disk1, disk2, rect3, rect4, inter1, inter2])
points, cells, _, _, _ = pygmsh.generate_mesh(geom)
ref = 1082.4470502181903
assert abs(compute_volume(points, cells) - ref) < 1.0e-2 * ref
return points, cells
if __name__ == "__main__":
from helpers import plot
plot("logo.png", *test())
# import meshio
# meshio.write_points_cells('logo.vtu', *test())
def train_ad(u_stab, V, alpha):
mesh = V.mesh()
# Define a neural network that will be added as a source term to the Stokes eqn
R = VectorFunctionSpace(mesh, "R", 0, dim=50)
W_1, W_2, b_1, b_2, W_3_1, W_3_2 = Function(R), Function(R), Function(
R), Function(R), Function(R), Function(R)
W_3 = as_vector([W_3_1, W_3_2])
R2 = VectorFunctionSpace(mesh, "R", 0, dim=2)
eps = 1e1
W_1.vector()[:] = eps * rand(R.dim())
W_2.vector()[:] = eps * rand(R.dim())
W_3[0].vector()[:] = eps * rand(R.dim())
W_3[1].vector()[:] = eps * rand(R.dim())
b_1.vector()[:] = eps * rand(R.dim())
b_2.vector()[:] = eps * rand(b_2.function_space().dim())
def nn(u, v):
#return inner(grad(p), grad(q)) * dx
def sigma_(vec, func=ufl.tanh):
v = [func(vec[i]) for i in range(vec.ufl_shape[0])]
return ufl.as_vector(v)
relu = lambda vec: conditional(ufl.gt(vec, 0), vec, (ufl.exp(vec) - 1))
sigma = lambda vec: sigma_(vec, func=relu) #lambda x:x)
#from IPython import embed
#embed()
n1 = dot(W_2, sigma(W_1 * u) + b_1)
n2 = dot(W_3_1, sigma(W_3_2 * u.dx(0)) + b_2)
return inner(n1, v) * dx + inner(n2, v.dx(0)) * dx, inner(
n1, n1) * dx + inner(n2, n2) * dx, n1
# Now solve the Stokes-NN forward problem
uh, reg = advection_diffusion(V, alpha, nn)
plot(uh, "out/ad0.png")
J = assemble((uh - u_stab)**2 * dx(domain=u_stab.function_space().mesh()))
print(f"J={J}", u_stab.function_space().ufl_element())
reg = 0
for W in [W_1, W_2, W_3_1, W_3_2, b_1, b_2]:
reg += 1E-2 * assemble(W**2 * dx)
J += reg
print(f"reg={reg}")
Jhat = ReducedFunctional(J, [
Control(W_1),
Control(b_1),
Control(b_2),
Control(W_2),
Control(W_3_1),
Control(W_3_2)
])
C_u = Control(uh)
set_log_level(LogLevel.ERROR)
minimize(Jhat,
tol=1e-200,
options={
"disp": True,
"gtol": 1e-12,
"maxiter": 50
})
print(
"|U - d| = ",
assemble(
inner(C_u.tape_value() - u_stab,
C_u.tape_value() - u_stab) *
dx(domain=u_stab.function_space().mesh()))**0.5)
u_nn = C_u.tape_value()
df.plot(u_nn, label='learned', marker='o')
df.plot(interpolate(u_stab, V), label='data alpha {}'.format(alpha))
df.plot(advection_diffusion(V, alpha=alpha, nn=None), label='no nn')
plt.legend()
plt.savefig("out/ad_nn.png")
return nn
@pytest.mark.skipif(pygmsh.get_gmsh_major_version() < 3,
reason='requires Gmsh >= 3')
def test():
geom = pygmsh.opencascade.Geometry(
characteristic_length_min=0.5,
characteristic_length_max=0.5,
)
container = geom.add_rectangle([0.0, 0.0, 0.0], 10.0, 10.0)
letter_i = geom.add_rectangle([2.0, 2.0, 0.0], 1.0, 4.5)
i_dot = geom.add_disk([2.5, 7.5, 0.0], 0.6)
disk1 = geom.add_disk([6.25, 4.5, 0.0], 2.5)
disk2 = geom.add_disk([6.25, 4.5, 0.0], 1.5)
letter_o = geom.boolean_difference([disk1], [disk2])
geom.boolean_difference([container], [letter_i, i_dot, letter_o])
points, cells, _, _, _ = pygmsh.generate_mesh(geom)
ref = 81.9131851877
assert abs(compute_volume(points, cells) - ref) < 1.0e-2 * ref
return points, cells
if __name__ == '__main__':
# import meshio
# meshio.write('m.vtu', *test())
from helpers import plot
plot('meshio_logo.png', *test())
def train_stokes(up_stab, ustab_elm):
mesh = up_stab.function_space().mesh()
W = FunctionSpace(mesh, ustab_elm)
# Now solve the Stokes with an unstable element pair,
# but with the NN as a source term
# Define a neural network that will be added as a source term to the Stokes eqn
R = VectorFunctionSpace(mesh, "R", 0, dim=50)
W_1, W_2, b_1, W_3_1, W_3_2 = Function(R), Function(R), Function(
R), Function(R), Function(R)
W_3 = as_vector([W_3_1, W_3_2])
R2 = VectorFunctionSpace(mesh, "R", 0, dim=2)
b_2 = Function(R2)
eps = 1e1
W_1.vector()[:] = eps * rand(R.dim())
W_2.vector()[:] = eps * rand(R.dim())
W_3[0].vector()[:] = eps * rand(R.dim())
W_3[1].vector()[:] = eps * rand(R.dim())
b_1.vector()[:] = eps * rand(R.dim())
b_2.vector()[:] = eps * rand(R2.dim())
def nn(u, p, v, q):
#return inner(grad(p), grad(q)) * dx
def sigma_(vec, func=ufl.tanh):
v = [func(vec[i]) for i in range(vec.ufl_shape[0])]
return ufl.as_vector(v)
relu = lambda vec: conditional(ufl.gt(vec, 0), vec, (ufl.exp(vec) - 1))
sigma = lambda vec: sigma_(vec, func=relu) #lambda x:x)
nn_p = dot(
W_3,
sigma(ufl.transpose(as_vector([W_1, W_2])) * grad(p) + b_1)) + b_2
#nn_q = dot(W_3, sigma(ufl.transpose(as_vector([W_1, W_2])) * grad(q) + b_1)) + b_2
return inner(nn_p, grad(q)) * dx, inner(nn_p, nn_p) * dx, nn_p
# Now solve the Stokes-NN forward problem
up, reg = stokes(W, nn)
u_nn, p_nn = up.split(deepcopy=True)
plot(u_nn, "out/u_nn0.png")
plot(p_nn, "out/p_nn0.png")
J = assemble((up - up_stab)**2 * dx)
print(f"J={J}")
# L2 regularisation
#J += 1e4*reg
#print(f"reg={1e4*reg}")
# l2 regularisation
reg = 0
for W in [W_1, W_2, b_1, W_3_1, W_3_2, b_2]:
reg += 1e4 * assemble(W**2 * dx)
J += reg
print(f"reg={reg}")
Jhat = ReducedFunctional(J, [
Control(W_1),
Control(b_1),
Control(W_2),
Control(b_2),
Control(W_3_1),
Control(W_3_2)
])
C_up = Control(up)
set_log_level(LogLevel.ERROR)
minimize(Jhat,
tol=1e-200,
options={
"disp": True,
"gtol": 1e-12,
"maxiter": 20
})
print(
"|U - d| = ",
assemble(
inner(C_up.tape_value() - up_stab,
C_up.tape_value() - up_stab) * dx)**0.5)
u_nn, p_nn = C_up.tape_value().split(deepcopy=True)
plot(u_nn, "out/u_nn.png")
plot(p_nn, "out/p_nn.png")
return nn
