def main():
# Create Neural Network
network = NeuralNetwork(inputDimension=2, hiddenLayers=[20, 20, 20, 20], activationFunction=ActivationFunction.Tanh)
# Load weights
# network.LoadWeights(path)
# Create PDE
laplace = Laplace_2d(frequency=6 * np.pi, network=network)
# Train
# laplace.Train(trainMode=TrainMode.DefaultAdaptive, iterations=20000)
# laplace.Train(trainMode=TrainMode.OptimalAdaptive, iterations=20000)
laplace.Train(trainMode=TrainMode.MagnitudeAdaptive, iterations=20000)
# Store weights
# network.SaveWeights(path)
laplace.ComputeL2Error()
laplace.ComputeMaxError()
# region Plots
# Surface plot
fig = plt.figure()
ax = fig.gca(projection='3d')
x, y, z = laplace.GetInteriorPlotData(pointCount=5000, tensor=network.yInt, x=[(0, 1), (0, 1)])
ax.plot_surface(x, y, z, cmap='viridis')
ax.set_xlabel("$x_1$")
ax.set_ylabel("$x_2$")
ax.set_zlabel("$u$")
# Boundary conditions
color = next(ax._get_lines.prop_cycler)['color']
x, y, z = laplace.GetBoundaryPlotData(pointCount=1000, tensor=network.boundaryCondition, x=[(0, 1), (0, 1)])
ax.plot3D(x[0], y[0], z[0], color=color, label="Boundary Condition")
for i in range(1, len(x)):
ax.plot3D(x[i], y[i], z[i], color=color)
# Single boundary plot
plt.figure()
x, y = laplace.GetInteriorPlotData(pointCount=1000, tensor=network.yInt, x=[(0, 1), 0.25])
plt.plot(x, y, label="Approximated Solution")
# Boundary conditions
x, y = laplace.GetBoundaryPlotData(pointCount=1000, tensor=network.boundaryCondition, x=[(0, 1), 0.25])
plt.scatter(x, y, label="Boundary Condition")
plt.xlabel("$x_1$")
plt.ylabel("$u$")
plt.legend()
plt.show()
# endregion
# Cleanup
network.Cleanup()
def main():
# Create Neural Network
network = NeuralNetwork(inputDimension=3,
hiddenLayers=[20, 20, 20, 20],
activationFunction=ActivationFunction.Tanh)
# Load weights
# network.LoadWeights(path)
# Create PDE
frequencies = [0, 4 * np.pi, 1 * np.pi]
frequencies[0] = np.sqrt(np.sum([freq**2 for freq in frequencies]))
laplace = Laplace_nd(frequencies=frequencies, network=network)
# Train
# laplace.Train(trainMode=TrainMode.DefaultAdaptive, iterations=20000)
# laplace.Train(trainMode=TrainMode.OptimalAdaptive, iterations=20000)
laplace.Train(trainMode=TrainMode.MagnitudeAdaptive, iterations=2000)
# Store weights
# network.SaveWeights(path)
laplace.ComputeL2Error()
laplace.ComputeMaxError()
# region Plots
# Plot approximation at x_1 = 0
fig = plt.figure()
ax = fig.gca(projection='3d')
x, y, z = laplace.GetInteriorPlotData(pointCount=5000,
tensor=network.yInt,
x=[0, (0, 1), (0, 1)])
ax.plot_surface(x, y, z, cmap='viridis')
ax.set_xlabel("$x_1$")
ax.set_ylabel("$x_2$")
ax.set_zlabel("$u$")
# Plot analytical solution at x_1 = 0
fig = plt.figure()
ax = fig.gca(projection='3d')
x, y, z = laplace.GetInteriorPlotData(pointCount=5000,
tensor=laplace.analyticalInterior,
x=[0, (0, 1), (0, 1)])
ax.plot_surface(x, y, z, cmap='viridis')
ax.set_xlabel("$x_1$")
ax.set_ylabel("$x_2$")
ax.set_zlabel("$u$")
# Plot boundary condition at x_1 = 0
fig = plt.figure()
ax = fig.gca(projection='3d')
x, y, z = laplace.GetBoundaryPlotData(pointCount=5000,
tensor=network.boundaryCondition,
x=[0, (0, 1), (0, 1)])
ax.plot_surface(x, y, z, cmap='viridis')
ax.set_xlabel("$x_1$")
ax.set_ylabel("$x_2$")
ax.set_zlabel("$u$")
# Plot solution and boundary conditions at x_3 = 0.5
fig = plt.figure()
ax = fig.gca(projection='3d')
x, y, z = laplace.GetInteriorPlotData(pointCount=5000,
tensor=network.yInt,
x=[(0, 1), (0, 1), 0.5])
ax.plot_surface(x, y, z, cmap='viridis')
ax.set_xlabel("$x_1$")
ax.set_ylabel("$x_2$")
ax.set_zlabel("$u$")
# Boundary conditions
color = next(ax._get_lines.prop_cycler)['color']
x, y, z = laplace.GetBoundaryPlotData(pointCount=1000,
tensor=network.boundaryCondition,
x=[(0, 1), (0, 1), 0.5])
ax.plot3D(x[0], y[0], z[0], color=color, label="Boundary Condition")
for i in range(1, len(x)):
ax.plot3D(x[i], y[i], z[i], color=color)
plt.show()
# endregion
# Cleanup
network.Cleanup()
