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from mpmath import chebyt, chop, taylor
from .problem import Problem
import torch
import torch.nn as nn
import numpy as np
from .cube import Cube
from .segment import Segment
from .deep_feed_forward import DeepFeedForward
from pina.label_tensor import LabelTensor
torch.pi = torch.acos(torch.zeros(1)).item() * 2 # which is 3.1415927410125732
class PINN(object):
def __init__(self,
problem,
model,
optimizer=torch.optim.Adam,
lr=0.001,
regularizer=0.00001,
data_weight=1.,
dtype=torch.float64,
device='cpu',
lr_accelerate=None,
error_norm='mse'):
'''
:param Problem problem: the formualation of the problem.
:param dict architecture: a dictionary containing the information to
build the model. Valid options are:
- inner_size [int] the number of neurons in the hidden layers; by
default is 20.
- n_layers [int] the number of hidden layers; by default is 4.
- func [nn.Module or str] the activation function; passing a `str`
is possible to chose adaptive function (between 'adapt_tanh'); by
default is non-adaptive iperbolic tangent.
:param float lr: the learning rate; default is 0.001
:param float regularizer: the coefficient for L2 regularizer term
:param type dtype: the data type to use for the model. Valid option are
`torch.float32` and `torch.float64` (`torch.float16` only on GPU);
default is `torch.float64`.
:param float lr_accelete: the coefficient that controls the learning
rate increase, such that, for all the epoches in which the loss is
decreasing, the learning_rate is update using
$learning_rate = learning_rate * lr_accelerate$.
When the loss stops to decrease, the learning rate is set to the
initial value [TODO test parameters]
'''
self.problem = problem
# self._architecture = architecture if architecture else dict()
# self._architecture['input_dimension'] = self.problem.domain_bound.shape[0]
# self._architecture['output_dimension'] = len(self.problem.variables)
# if hasattr(self.problem, 'params_domain'):
# self._architecture['input_dimension'] += self.problem.params_domain.shape[0]
self.accelerate = lr_accelerate
self.error_norm = error_norm
if device == 'cuda' and not torch.cuda.is_available():
raise RuntimeError
self.device = torch.device(device)
self.dtype = dtype
self.history = []
self.model = model
self.model.to(dtype=self.dtype, device=self.device)
self.input_pts = {}
self.truth_values = {}
self.trained_epoch = 0
self.optimizer = optimizer(
self.model.parameters(), lr=lr, weight_decay=regularizer)
self.data_weight = data_weight
@property
def problem(self):
return self._problem
@problem.setter
def problem(self, problem):
if not isinstance(problem, Problem):
raise TypeError
self._problem = problem
def get_data_residuals(self):
data_residuals = []
for output in self.data_pts:
data_values_pred = self.model(self.data_pts[output])
data_residuals.append(data_values_pred - self.data_values[output])
return torch.cat(data_residuals)
def get_phys_residuals(self):
"""
"""
residuals = []
for equation in self.problem.equation:
residuals.append(equation(self.phys_pts, self.model(self.phys_pts)))
return residuals
def _compute_norm(self, vec):
"""
Compute the norm of the `vec` one-dimensional tensor based on the
`self.error_norm` attribute.
.. todo: complete
:param vec torch.tensor: the tensor
"""
if isinstance(self.error_norm, int):
return torch.sum(torch.abs(vec**self.error_norm))**(1./self.error_norm)
elif self.error_norm == 'mse':
return torch.mean(vec**2)
elif self.error_norm == 'me':
return torch.mean(torch.abs(vec))
else:
raise RuntimeError
def save_state(self, filename):
checkpoint = {
'epoch': self.trained_epoch,
'model_state': self.model.state_dict(),
'optimizer_state' : self.optimizer.state_dict(),
'optimizer_class' : self.optimizer.__class__,
'history' : self.history,
}
# TODO save also architecture param?
#if isinstance(self.model, DeepFeedForward):
# checkpoint['model_class'] = self.model.__class__
# checkpoint['model_structure'] = {
# }
torch.save(checkpoint, filename)
def load_state(self, filename):
checkpoint = torch.load(filename)
self.model.load_state_dict(checkpoint['model_state'])
self.optimizer = checkpoint['optimizer_class'](self.model.parameters())
self.optimizer.load_state_dict(checkpoint['optimizer_state'])
self.trained_epoch = checkpoint['epoch']
self.history = checkpoint['history']
print(self.history)
return self
def span_pts(self, n, mode='grid', locations='all'):
'''
'''
if locations == 'all':
locations = [condition for condition in self.problem.conditions]
for location in locations:
manifold, func = self.problem.conditions[location].values()
if torch.is_tensor(manifold):
pts = manifold
else:
pts = manifold.discretize(n, mode)
pts = torch.from_numpy(pts)
self.input_pts[location] = LabelTensor(pts, self.problem.input_variables)
self.input_pts[location].tensor.to(dtype=self.dtype, device=self.device)
self.input_pts[location].tensor.requires_grad_(True)
self.input_pts[location].tensor.retain_grad()
def plot_pts(self, locations='all'):
import matplotlib
matplotlib.use('GTK3Agg')
import matplotlib.pyplot as plt
if locations == 'all':
locations = [condition for condition in self.problem.conditions]
for location in locations:
x, y = self.input_pts[location].tensor.T
#plt.plot(x.detach(), y.detach(), 'o', label=location)
np.savetxt('burgers_{}_pts.txt'.format(location), self.input_pts[location].tensor.detach(), header='x y', delimiter=' ')
gggg
plt.legend()
plt.show()
def train(self, stop=100, frequency_print=2, trial=None):
epoch = 0
while True:
losses = []
for condition_name in self.problem.conditions:
pts = self.input_pts[condition_name]
predicted = self.model(pts.tensor)
if isinstance(self.problem.conditions[condition_name]['func'], list):
for func in self.problem.conditions[condition_name]['func']:
residuals = func(pts, predicted)
losses.append(self._compute_norm(residuals))
else:
residuals = self.problem.conditions[condition_name]['func'](pts, predicted)
losses.append(self._compute_norm(residuals))
#print(condition_name, losses[-1])
self.optimizer.zero_grad()
sum(losses).backward()
self.optimizer.step()
self.trained_epoch += 1
if epoch % 50 == 0:
self.history.append([loss.detach().item() for loss in losses])
epoch += 1
if trial:
import optuna
trial.report(loss[0].item()+loss[1].item(), epoch)
if trial.should_prune():
raise optuna.exceptions.TrialPruned()
if isinstance(stop, int):
if epoch == stop:
break
elif isinstance(stop, float):
if sum(losses) < stop:
break
if epoch % frequency_print == 0:
print('[epoch {:05d}] {:.6e} '.format(self.trained_epoch, sum(losses).item()), end='')
for loss in losses:
print('{:.6e} '.format(loss), end='')
print()
return sum(losses).item()
def error(self, dtype='l2', res=100):
import numpy as np
if hasattr(self.problem, 'truth_solution') and self.problem.truth_solution is not None:
pts_container = []
for mn, mx in self.problem.domain_bound:
pts_container.append(np.linspace(mn, mx, res))
grids_container = np.meshgrid(*pts_container)
Z_true = self.problem.truth_solution(*grids_container)
elif hasattr(self.problem, 'data_solution') and self.problem.data_solution is not None:
grids_container = self.problem.data_solution['grid']
Z_true = self.problem.data_solution['grid_solution']
try:
unrolled_pts = torch.tensor([t.flatten() for t in grids_container]).T.to(dtype=self.dtype, device=self.device)
Z_pred = self.model(unrolled_pts)
Z_pred = Z_pred.detach().numpy().reshape(grids_container[0].shape)
if dtype == 'l2':
return np.linalg.norm(Z_pred - Z_true)/np.linalg.norm(Z_true)
else:
# TODO H1
pass
except:
print("")
print("Something went wrong...")
print("Not able to compute the error. Please pass a data solution or a true solution")
def plot(self, res, filename=None, variable=None):
'''
'''
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
pts_container = []
#for mn, mx in [[-1, 1], [-1, 1]]:
for mn, mx in [[0, 1], [0, 1]]:
#for mn, mx in [[-1, 1], [0, 1]]:
pts_container.append(np.linspace(mn, mx, res))
grids_container = np.meshgrid(*pts_container)
unrolled_pts = torch.tensor([t.flatten() for t in grids_container]).T
unrolled_pts.to(dtype=self.dtype)
Z_pred = self.model(unrolled_pts)
#######################################################
# poisson
# Z_truth = self.problem.truth_solution(unrolled_pts[:, 0], unrolled_pts[:, 1])
# Z_pred = Z_pred.tensor.detach().reshape(grids_container[0].shape)
# Z_truth = Z_truth.detach().reshape(grids_container[0].shape)
# err = np.abs(Z_pred-Z_truth)
# with open('poisson2_nofeat_plot.txt', 'w') as f_:
# f_.write('x y truth pred e\n')
# for (x, y), tru, pre, e in zip(unrolled_pts, Z_truth.reshape(-1, 1), Z_pred.reshape(-1, 1), err.reshape(-1, 1)):
# f_.write('{} {} {} {} {}\n'.format(x.item(), y.item(), tru.item(), pre.item(), e.item()))
# n = Z_pred.shape[1]
# plt.figure(figsize=(16, 6))
# plt.subplot(1, 3, 1)
# plt.contourf(*grids_container, Z_truth)
# plt.colorbar()
# plt.subplot(1, 3, 2)
# plt.contourf(*grids_container, Z_pred)
# plt.colorbar()
# plt.subplot(1, 3, 3)
# plt.contourf(*grids_container, err)
# plt.colorbar()
# plt.show()
#######################################################
# burgers
import scipy
data = scipy.io.loadmat('Data/burgers_shock.mat')
data_solution = {'grid': np.meshgrid(data['x'], data['t']), 'grid_solution': data['usol'].T}
grids_container = data_solution['grid']
print(data_solution['grid_solution'].shape)
unrolled_pts = torch.tensor([t.flatten() for t in grids_container]).T
unrolled_pts.to(dtype=self.dtype)
Z_pred = self.model(unrolled_pts)
Z_truth = data_solution['grid_solution']
Z_pred = Z_pred.tensor.detach().reshape(grids_container[0].shape)
print(Z_pred, Z_truth)
err = np.abs(Z_pred.numpy()-Z_truth)
with open('burgers_nofeat_plot.txt', 'w') as f_:
f_.write('x y truth pred e\n')
for (x, y), tru, pre, e in zip(unrolled_pts, Z_truth.reshape(-1, 1), Z_pred.reshape(-1, 1), err.reshape(-1, 1)):
f_.write('{} {} {} {} {}\n'.format(x.item(), y.item(), tru.item(), pre.item(), e.item()))
n = Z_pred.shape[1]
plt.figure(figsize=(16, 6))
plt.subplot(1, 3, 1)
plt.contourf(*grids_container, Z_truth,vmin=-1, vmax=1)
plt.colorbar()
plt.subplot(1, 3, 2)
plt.contourf(*grids_container, Z_pred, vmin=-1, vmax=1)
plt.colorbar()
plt.subplot(1, 3, 3)
plt.contourf(*grids_container, err)
plt.colorbar()
plt.show()
# for i, output in enumerate(Z_pred.tensor.T, start=1):
# output = output.detach().numpy().reshape(grids_container[0].shape)
# plt.subplot(1, n, i)
# plt.contourf(*grids_container, output)
# plt.colorbar()
if filename is None:
plt.show()
else:
plt.savefig(filename)
def plot_params(self, res, param, filename=None, variable=None):
'''
'''
import matplotlib
matplotlib.use('GTK3Agg')
import matplotlib.pyplot as plt
if hasattr(self.problem, 'truth_solution') and self.problem.truth_solution is not None:
n_plot = 2
elif hasattr(self.problem, 'data_solution') and self.problem.data_solution is not None:
n_plot = 2
else:
n_plot = 1
fig, axs = plt.subplots(nrows=1, ncols=n_plot, figsize=(n_plot*6,4))
if not isinstance(axs, np.ndarray): axs = [axs]
if hasattr(self.problem, 'data_solution') and self.problem.data_solution is not None:
grids_container = self.problem.data_solution['grid']
Z_true = self.problem.data_solution['grid_solution']
elif hasattr(self.problem, 'truth_solution') and self.problem.truth_solution is not None:
pts_container = []
for mn, mx in self.problem.domain_bound:
pts_container.append(np.linspace(mn, mx, res))
grids_container = np.meshgrid(*pts_container)
Z_true = self.problem.truth_solution(*grids_container)
pts_container = []
for mn, mx in self.problem.domain_bound:
pts_container.append(np.linspace(mn, mx, res))
grids_container = np.meshgrid(*pts_container)
unrolled_pts = torch.tensor([t.flatten() for t in grids_container]).T.to(dtype=self.type)
#print(unrolled_pts)
#print(param)
param_unrolled_pts = torch.cat((unrolled_pts, param.repeat(unrolled_pts.shape[0], 1)), 1)
if variable==None:
variable = self.problem.variables[0]
Z_pred = self.evaluate(param_unrolled_pts)[variable]
variable = "Solution"
else:
Z_pred = self.evaluate(param_unrolled_pts)[variable]
Z_pred= Z_pred.detach().numpy().reshape(grids_container[0].shape)
set_pred = axs[0].contourf(*grids_container, Z_pred)
axs[0].set_title('PINN [trained epoch = {}]'.format(self.trained_epoch) + " " + variable) #TODO add info about parameter in the title
fig.colorbar(set_pred, ax=axs[0])
if n_plot == 2:
set_true = axs[1].contourf(*grids_container, Z_true)
axs[1].set_title('Truth solution')
fig.colorbar(set_true, ax=axs[1])
if filename is None:
plt.show()
else:
fig.savefig(filename + " " + variable)
def plot_error(self, res, filename=None):
import matplotlib
matplotlib.use('GTK3Agg')
import matplotlib.pyplot as plt
fig, axs = plt.subplots(nrows=1, ncols=1, figsize=(6,4))
if not isinstance(axs, np.ndarray): axs = [axs]
if hasattr(self.problem, 'data_solution') and self.problem.data_solution is not None:
grids_container = self.problem.data_solution['grid']
Z_true = self.problem.data_solution['grid_solution']
elif hasattr(self.problem, 'truth_solution') and self.problem.truth_solution is not None:
pts_container = []
for mn, mx in self.problem.domain_bound:
pts_container.append(np.linspace(mn, mx, res))
grids_container = np.meshgrid(*pts_container)
Z_true = self.problem.truth_solution(*grids_container)
try:
unrolled_pts = torch.tensor([t.flatten() for t in grids_container]).T.to(dtype=self.type)
Z_pred = self.model(unrolled_pts)
Z_pred = Z_pred.detach().numpy().reshape(grids_container[0].shape)
set_pred = axs[0].contourf(*grids_container, abs(Z_pred - Z_true))
axs[0].set_title('PINN [trained epoch = {}]'.format(self.trained_epoch) + "Pointwise Error")
fig.colorbar(set_pred, ax=axs[0])
if filename is None:
plt.show()
else:
fig.savefig(filename)
except:
print("")
print("Something went wrong...")
print("Not able to plot the error. Please pass a data solution or a true solution")
'''
print(self.pred_loss.item(),loss.item(), self.old_loss.item())
if self.accelerate is not None:
if self.pred_loss > loss and loss >= self.old_loss:
self.current_lr = self.original_lr
#print('restart')
elif (loss-self.pred_loss).item() < 0.1:
self.current_lr += .5*self.current_lr
#print('powa')
else:
self.current_lr -= .5*self.current_lr
#print(self.current_lr)
#self.current_lr = min(loss.item()*3, 0.02)
for g in self.optimizer.param_groups:
g['lr'] = self.current_lr
'''