lambda_ = LOCAL_TIME_GRID_SIZE / LOCAL_SPACE_GRID_SIZE
numerical_flux = LaxFriedrichsFlux(linear_transport_flux,
linear_transport_flux_derivative, lambda_)
discretization = DiscontinuousGalerkin(numerical_flux, inverse_transformation,
LOCAL_SPACE_GRID_SIZE)
grid_operator = GridOperator(space_time_grid,
discretization,
DGFunction,
u_0_function,
TimeStepperType=RungeKutta4,
local_space_grid_size=LOCAL_SPACE_GRID_SIZE,
local_time_grid_size=LOCAL_TIME_GRID_SIZE)
fom = SpacetimeModel(grid_operator, inverse_transformation, n_x=N_X, n_t=N_T)
N_train = 5
parameters = np.linspace(0.25, 1., N_train)
reference_parameter = 1.
gs_smoothing_params = {'alpha': 1000., 'exponent': 3}
registration_params = {'sigma': 0.1, 'epsilon': 0.1, 'iterations': 1500}
restarts = 10
reductor = NonlinearNeuralNetworkReductor(
fom,
parameters,
reference_parameter,
gs_smoothing_params=gs_smoothing_params)
rom, output_dict = reductor.reduce(return_all=True,
lambda_ = LOCAL_TIME_GRID_SIZE / LOCAL_SPACE_GRID_SIZE
numerical_flux = LaxFriedrichsFlux(linear_transport_flux,
linear_transport_flux_derivative, lambda_)
discretization = DiscontinuousGalerkin(numerical_flux, inverse_transformation,
LOCAL_SPACE_GRID_SIZE)
grid_operator = GridOperator(space_time_grid,
discretization,
DGFunction,
u_0_function,
TimeStepperType=RungeKutta4,
local_space_grid_size=LOCAL_SPACE_GRID_SIZE,
local_time_grid_size=LOCAL_TIME_GRID_SIZE)
fom = SpacetimeModel(grid_operator, inverse_transformation, n_x=N_X, n_t=N_T)
parameters = []
reference_parameter = 1.
gs_smoothing_params = {'alpha': 100., 'exponent': 3}
registration_params = {'sigma': 0.1, 'epsilon': 0.1, 'iterations': 5000}
trainer_params = {'learning_rate': 0.001}
training_params = {'number_of_epochs': int(1e5)}
restarts = 100
NUM_WORKERS = 2
MAX_BASIS_SIZE = 10
reductor = NonlinearNeuralNetworkReductor(
fom,
space_time_grid = perform_tent_pitching(grid,
T_MAX,
characteristic_speed,
n_max=1000)
lambda_ = LOCAL_TIME_GRID_SIZE / LOCAL_SPACE_GRID_SIZE
numerical_flux = LaxFriedrichsFlux(linear_transport_flux,
linear_transport_flux_derivative, lambda_)
discretization = DiscontinuousGalerkin(numerical_flux, inverse_transformation,
LOCAL_SPACE_GRID_SIZE)
grid_operator = GridOperator(space_time_grid,
discretization,
DGFunction,
u_0_function,
TimeStepperType=RungeKutta4,
local_space_grid_size=LOCAL_SPACE_GRID_SIZE,
local_time_grid_size=LOCAL_TIME_GRID_SIZE)
fom = SpacetimeModel(grid_operator, inverse_transformation, n_x=N_X, n_t=N_T)
N_train = 20
parameters = np.linspace(0.25, 1., N_train)
full_solutions = [(mu, fom.solve(mu)) for mu in parameters]
with open('outputs/full_solutions', 'wb') as output_file:
pickle.dump(full_solutions, output_file)