def lorenz_coefficients(normalization, poly_order=3):
sigma = 10
beta = 8 / 3
rho = 28
Xi = np.zeros((library_size(3, poly_order), 3))
Xi[1, 0] = -sigma
Xi[2, 0] = sigma * normalization[0] / normalization[1]
Xi[1, 1] = rho * normalization[1] / normalization[0]
Xi[2, 1] = -1
Xi[6, 1] = -normalization[1] / (normalization[0] * normalization[2])
Xi[3, 2] = -beta
Xi[5, 2] = normalization[2] / (normalization[0] * normalization[1])
return Xi
def lorenz_coefficients(normalization, poly_order=3, sigma=10., beta=8/3, rho=28.):
"""
Generate the SINDy coefficient matrix for the Lorenz system.
Arguments:
normalization - 3-element list of array specifying scaling of each Lorenz variable
poly_order - Polynomial order of the SINDy model.
sigma, beta, rho - Parameters of the Lorenz system
"""
Xi = np.zeros((library_size(3,poly_order),3))
Xi[1,0] = -sigma
Xi[2,0] = sigma*normalization[0]/normalization[1]
Xi[1,1] = rho*normalization[1]/normalization[0]
Xi[2,1] = -1
Xi[6,1] = -normalization[1]/(normalization[0]*normalization[2])
Xi[3,2] = -beta
Xi[5,2] = normalization[2]/(normalization[0]*normalization[1])
return Xi
def get_params_tf(training_data, hyper_params):
params = {}
params['input_dim'] = 128
params['latent_dim'] = 3
params['model_order'] = 1
params['poly_order'] = 3
params['include_sine'] = False
params['library_dim'] = library_size(params['latent_dim'],
params['poly_order'],
params['include_sine'], True)
# sequential thresholding parameters
params['sequential_thresholding'] = True
params['coefficient_threshold'] = hyper_params['threshold']
params['threshold_frequency'] = hyper_params['threshold_freq']
params['coefficient_mask'] = np.ones(
(params['library_dim'], params['latent_dim']))
params['coefficient_initialization'] = 'constant'
# loss function weighting
params['loss_weight_decoder'] = 1.0
params['loss_weight_sindy_z'] = hyper_params['eta2']
params['loss_weight_sindy_x'] = hyper_params['eta1']
params['loss_weight_sindy_regularization'] = hyper_params['eta3']
params['activation'] = 'sigmoid'
params['widths'] = [64, 32]
# training parameters
params['epoch_size'] = training_data['x'].shape[0]
params['batch_size'] = hyper_params['batch_size']
params['learning_rate'] = hyper_params['lr']
params['data_path'] = os.getcwd() + '/'
params['print_progress'] = True
params['print_frequency'] = hyper_params['model_eval']
# training time cutoffs
params['max_epochs'] = hyper_params['epochs']
params['refinement_epochs'] = hyper_params['epochs_refinement']
return params
from training import train_network
import tensorflow as tf
# SET UP PARAMETERS
params = {}
# generate training, validation, testing data
training_data = get_pendulum_data(100)
validation_data = get_pendulum_data(10)
params['N'] = training_data['x'].shape[-1]
params['d'] = 1
params['model_order'] = 2
params['poly_order'] = 3
params['include_sine'] = True
params['l'] = library_size(2 * params['d'], params['poly_order'],
params['include_sine'], True)
# set up sequential thresholding
params['sequential_thresholding'] = True
params['coefficient_threshold'] = 0.1
params['threshold_frequency'] = 500
params['coefficient_mask'] = np.ones((params['l'], params['d']))
params['coefficient_initialization'] = 'constant'
# define loss weights
params['loss_weight_decoder'] = 1.0
params['loss_weight_sindy_x'] = 5e-4
params['loss_weight_sindy_z'] = 5e-5
params['loss_weight_sindy_regularization'] = 1e-5
params['activation'] = 'sigmoid'
from training import train_network
import tensorflow as tf
# generate training, validation, testing data
noise_strength = 1e-6
training_data = get_lorenz_data(1024, noise_strength=noise_strength)
validation_data = get_lorenz_data(20, noise_strength=noise_strength)
params = {}
params['input_dim'] = 128
params['latent_dim'] = 3
params['model_order'] = 1
params['poly_order'] = 3
params['include_sine'] = False
params['library_dim'] = library_size(params['latent_dim'], params['poly_order'], params['include_sine'], True)
# sequential thresholding parameters
params['sequential_thresholding'] = True
params['coefficient_threshold'] = 0.1
params['threshold_frequency'] = 500
params['coefficient_mask'] = np.ones((params['library_dim'], params['latent_dim']))
params['coefficient_initialization'] = 'constant'
# loss function weighting
params['loss_weight_decoder'] = 1.0
params['loss_weight_sindy_z'] = 0.0
params['loss_weight_sindy_x'] = 1e-4
params['loss_weight_sindy_regularization'] = 1e-5
params['activation'] = 'sigmoid'
from training import train_network
import tensorflow as tf
# SET UP PARAMETERS
params = {}
# generate training, validation, testing data
training_data = get_lorenz_data(2048)
validation_data = get_lorenz_data(20)
params['N'] = 128
params['d'] = 3
params['model_order'] = 1
params['poly_order'] = 3
params['include_sine'] = False
params['l'] = library_size(params['d'], params['poly_order'], False, True)
# set up sequential thresholding
params['sequential_thresholding'] = True
params['coefficient_threshold'] = 0.1
params['threshold_frequency'] = 500
params['coefficient_mask'] = np.ones((params['l'], params['d']))
params['coefficient_initialization'] = 'constant'
# define loss weights
params['loss_weight_decoder'] = 1.0
params['loss_weight_sindy_z'] = 0.0
params['loss_weight_sindy_x'] = 1e-4
params['loss_weight_sindy_regularization'] = 1e-5
params['activation'] = 'sigmoid'
def create_data_frame(self, hyper_params_grid):
"""Takes a dictionary of hyperparameters. Every entry an be a list or a scaler.
Every list must have the same length. hyper_params_fix are the default values.
They can be changed with hyper_params_grid. If they are not changed, for all hyper_params the
default values are set.
Args:
hyper_params_grid (dict): hyperparameters to use.
Returns:
pandas.Dataframe: Hyperparameters for different models.
"""
hyper_params_fix = {
'stop_criterion': ['best_score'],
'lr': [1e-3],
'alpha': [0.01],
'epochs': [0],
'epochs_refinement': [0],
'model_name': ['IV'],
'steps_inner': [20],
'batch_size': [1000],
'z_latent': [3],
'num_train_examples': [50],
'num_val_examples': [50],
'eta1': [1e-4],
'eta2': [0],
'eta3': [1e-5],
'poly_order': [3],
'model_eval': [500],
'step_sample': [10],
'include_sine': [False],
'shuffle': [True],
'threshold': [0.1],
'threshold_freq': [500],
'num_simulations': [20],
'activate_thresholding': [True],
'refinement': [False],
'stop_best_score': [6],
'training_set': [0],
'train_num_simulations': [20]
}
hyper_params_fix['library_dim'] = [
library_size(hyper_params_fix['z_latent'][0],
hyper_params_fix['poly_order'][0],
hyper_params_fix['include_sine'][0])
]
n = 0
# search number of models
for key in hyper_params_grid.keys():
hyper_params_fix[key] = hyper_params_grid[key]
if len(hyper_params_fix[key]) > n:
n = len(hyper_params_fix[key])
# set default hyper_params for every model
for key in hyper_params_fix.keys():
if len(hyper_params_fix[key]) == n:
continue
else:
hyper_params_fix[key] = np.repeat(hyper_params_fix[key], n)
df = pd.DataFrame(hyper_params_fix)
return df
POLYORDER = 2
INCLUDE_SIN = False
LATENT_DIM = 2
device = 'cuda:0'
training, val, testing = get_rd_data(random=True)
trainset = RDDataset(training)
testset = RDDataset(testing)
trainloader = DataLoader(trainset,
batch_size=8,
shuffle=True,
num_workers=0)
testloader = DataLoader(testset,
batch_size=8,
shuffle=False,
num_workers=0)
model = CNNAutoEncoder(latent_dim=LATENT_DIM)
model.to(device)
library_n = library_size(LATENT_DIM,
POLYORDER,
use_sine=INCLUDE_SIN,
include_constant=True)
sindy_model = nn.Linear(library_n, LATENT_DIM, bias=False)
sindy_model.to(device)
evaluate(model, sindy_model, trainloader, train=True, device=device)
