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