466 lines
18 KiB
Python
466 lines
18 KiB
Python
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 .deep_feed_forward import DeepFeedForward
|
|
from pina.label_tensor import LabelTensor
|
|
from pina.pinn import PINN
|
|
torch.pi = torch.acos(torch.zeros(1)).item() * 2 # which is 3.1415927410125732
|
|
|
|
class ParametricPINN(PINN):
|
|
|
|
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__,
|
|
}
|
|
|
|
# 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']
|
|
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 train(self, stop=100, frequency_print=2, trial=None):
|
|
|
|
epoch = 0
|
|
|
|
## TODO for elliptic
|
|
# parameters = torch.cat(torch.linspace(
|
|
# self.problem.parameter_domain[0, 0],
|
|
# self.problem.parameter_domain[0, 1],
|
|
# 5)
|
|
|
|
## for param laplacian
|
|
#parameters = torch.rand(50, 2)*2-1
|
|
parameters = torch.from_numpy(Cube([[-1, 1], [-1, 1]]).discretize(5, 'grid'))
|
|
# alpha_p = torch.logspace(start=-2, end=0, steps=10)
|
|
# mu_p = torch.linspace(0.5, 3, 5)
|
|
# g1_, g2_ = torch.meshgrid(alpha_p, mu_p)
|
|
# parameters = torch.cat([g2_.reshape(-1, 1), g1_.reshape(-1, 1)], axis=1)
|
|
print(parameters)
|
|
|
|
while True:
|
|
|
|
losses = []
|
|
|
|
for condition_name in self.problem.conditions:
|
|
|
|
pts = self.input_pts[condition_name]
|
|
pts = torch.cat([
|
|
pts.tensor.repeat_interleave(parameters.shape[0], dim=0),
|
|
torch.tile(parameters, (pts.tensor.shape[0], 1))
|
|
], axis=1)
|
|
pts = LabelTensor(pts, self.problem.input_variables + self.problem.parameters)
|
|
predicted = self.model(pts.tensor)
|
|
#predicted = self.model(pts)
|
|
|
|
if isinstance(self.problem.conditions[condition_name]['func'], list):
|
|
for func in self.problem.conditions[condition_name]['func']:
|
|
residuals = func(pts, None, predicted)
|
|
losses.append(self._compute_norm(residuals))
|
|
else:
|
|
residuals = self.problem.conditions[condition_name]['func'](pts, None, predicted)
|
|
losses.append(self._compute_norm(residuals))
|
|
self.optimizer.zero_grad()
|
|
sum(losses).backward()
|
|
self.optimizer.step()
|
|
|
|
#for p in parameters:
|
|
# pts = self.input_pts[condition_name]
|
|
# #pts = torch.cat([pts.tensor, p.double().repeat(pts.tensor.shape[0]).reshape(-1, 2)], axis=1)
|
|
# #pts = torch.cat([pts.tensor, p.double().repeat(pts.tensor.shape[0]).reshape(-1, 1)], axis=1)
|
|
# #print(self.problem.input_variables)
|
|
# # print(self.problem.parameters)
|
|
# # print(pts.shape)
|
|
# print(pts.tensor.repeat_interleave(parameters.shape[0]))
|
|
# # print(pts)
|
|
# # gg
|
|
# a = torch.cat([
|
|
# pts.tensor.repeat_interleave(parameters.shape[0], dim=0),
|
|
# torch.tile(parameters, (pts.tensor.shape[0], 1))
|
|
# ], axis=1)
|
|
# for i in a:
|
|
# print(i.detach())
|
|
# ttt
|
|
# pts = LabelTensor(pts, self.problem.input_variables + self.problem.parameters)
|
|
|
|
|
|
# ffff
|
|
# print(pts.labels)
|
|
|
|
# predicted = self.model(pts.tensor)
|
|
# #predicted = self.model(pts)
|
|
# if isinstance(self.problem.conditions[condition_name]['func'], list):
|
|
# for func in self.problem.conditions[condition_name]['func']:
|
|
# residuals = func(pts, LabelTensor(p.reshape(1, -1), ['mu', 'alpha']), predicted)
|
|
# tmp_losses.append(self._compute_norm(residuals))
|
|
# else:
|
|
# residuals = self.problem.conditions[condition_name]['func'](pts, p, predicted)
|
|
# tmp_losses.append(self._compute_norm(residuals))
|
|
#losses.append(sum(tmp_losses))
|
|
|
|
|
|
self.trained_epoch += 1
|
|
#if epoch % 10 == 0:
|
|
# self.history.append(losses)
|
|
|
|
epoch += 1
|
|
|
|
if trial:
|
|
import optuna
|
|
rial.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 loss[0].item() + loss[1].item() < 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, param, filename=None, variable=None):
|
|
'''
|
|
'''
|
|
import matplotlib
|
|
matplotlib.use('GTK3Agg')
|
|
import matplotlib.pyplot as plt
|
|
|
|
pts_container = []
|
|
for mn, mx in [[-1, 1], [-1, 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 = torch.cat([unrolled_pts, param.double().repeat(unrolled_pts.shape[0]).reshape(-1, 2)], axis=1)
|
|
|
|
unrolled_pts.to(dtype=self.dtype)
|
|
unrolled_pts = LabelTensor(unrolled_pts, ['x1', 'x2', 'mu1', 'mu2'])
|
|
|
|
Z_pred = self.model(unrolled_pts.tensor)
|
|
n = Z_pred.tensor.shape[1]
|
|
plt.figure(figsize=(6*n, 6))
|
|
|
|
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
|
|
'''
|