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vanilla.py
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import json
import math
import os
from datetime import datetime
from math import log, floor, isnan
from collections import defaultdict
import torch.nn.functional as F
from torch.autograd import grad
import torch.optim.lr_scheduler as schedulers
from torch import optim
from torch import nn
import torch
from torch.nn import MSELoss
from network import W
import numpy as np
import matplotlib.pyplot as plt
from scipy.io import loadmat
from scipy.interpolate import griddata
import time
from itertools import product, combinations
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
from mpl_toolkits.axes_grid1 import make_axes_locatable
import matplotlib.gridspec as gridspec
torch.manual_seed(0)
# CUDA support
if torch.cuda.is_available():
device = torch.device('cuda')
pytorch_device = torch.device('cuda')
device_string = "cuda"
torch.cuda.manual_seed_all(0)
else:
device = torch.device('cpu')
device_string = "cpu"
print(f"Device being used: {device}")
class Trainer:
def __init__(self, config=None, **kwargs):
self.lr = config['lr']
self.epochs = config['epochs']
self.__dict__.update(kwargs)
self.logged_results = defaultdict(list)
self.w = W(config)
if self.verbosity:
print(self.w, '\n')
# interior points
self.x_interior = torch.vstack([self.x_i.clone()])
self.y_interior = torch.vstack([self.y_i.clone()])
self.X_interior = torch.hstack([self.x_interior, self.y_interior])
# interior and boundary points
self.x_tilde = torch.vstack([self.x_i.clone(), self.x_b.clone()])
self.y_tilde = torch.vstack([self.y_i.clone(), self.y_b.clone()])
self.X_tilde = torch.hstack([self.x_tilde, self.y_tilde])
# interior, boundary, and ghost points
self.x_full = torch.vstack([self.x_i.clone(), self.x_b.clone(), self.x_g.clone()])
self.y_full = torch.vstack([self.y_i.clone(), self.y_b.clone(), self.y_g.clone()])
self.X_full = torch.hstack([self.x_full, self.y_full])
# boundary points
self.X_b = torch.hstack([self.x_b.clone(), self.y_b.clone()])
if config['optimizer'] == 'adam':
self.optimizer_choice = optim.Adam
elif config['optimizer'] == 'lbfgs':
self.optimizer_choice = optim.LBFGS
elif config['optimizer'] == 'sgd':
self.optimizer_choice = optim.SGD
self.optimizer = self.optimizer_choice(self.w.parameters(), lr=self.lr)
@staticmethod
def compute_mse(a, b):
mse = MSELoss()(torch.flatten(a), torch.flatten(b))
return mse.item()
@staticmethod
def compute_l2(a, b):
diff = torch.subtract(torch.flatten(a).detach().cpu(), torch.flatten(b).detach().cpu())
relative_l2_error = torch.linalg.norm(diff) / torch.linalg.norm(torch.flatten(b))
return relative_l2_error.item()
@staticmethod
def compute_linf(a):
return torch.linalg.norm(a.to(PRECISION), ord=float('inf')).item()
def train(self):
epochs = self.epochs
self.u_tilde = self.u[:self.ib_idx] # interior + boundary
self.f_interior = self.f[:self.b_starts] # only interior
if device_string == "cuda":
torch.cuda.synchronize() # first call to get all cuda tensors on GPU
start = time.perf_counter()
for i in range(1, epochs + 1):
try:
def closure():
self.optimizer.zero_grad()
# residual term on interior points only
u_pred_interior = self.w.forward(self.X_interior)
u_x = grad(u_pred_interior, self.x_interior, grad_outputs=torch.ones_like(
u_pred_interior), create_graph=True, retain_graph=True)[0]
u_xx = grad(u_x, self.x_interior, grad_outputs=torch.ones_like(
u_pred_interior), create_graph=True, retain_graph=True)[0]
u_y = grad(u_pred_interior, self.y_interior, grad_outputs=torch.ones_like(
u_pred_interior), create_graph=True, retain_graph=True)[0]
u_yy = grad(u_y, self.y_interior, grad_outputs=torch.ones_like(
u_pred_interior), create_graph=True, retain_graph=True)[0]
# Poisson residual
f_pred = (u_xx + u_yy) - self.f_interior
boundary_pred = self.w.forward(self.X_b)
# first partial derivatives on the boundary
l2_w_x = grad(boundary_pred, self.x_b, grad_outputs=torch.ones_like(boundary_pred),
create_graph=True, retain_graph=True)[0]
l2_w_y = grad(boundary_pred, self.y_b, grad_outputs=torch.ones_like(boundary_pred),
create_graph=True, retain_graph=True)[0]
# combining the partial derivatives
w_xy = torch.hstack([l2_w_x, l2_w_y])
# element wise dot product between the normal vectors and first partial derivatives
gradient_n = torch.multiply(self.n, w_xy).sum(dim=1).unsqueeze(dim=1)
# loss on the boundary
boundary_loss_term = torch.multiply(self.alpha, gradient_n) + \
torch.multiply(self.beta, boundary_pred) - self.g
l2 = torch.mean(torch.square(torch.flatten(f_pred)))
l3 = torch.mean(torch.square(torch.flatten(boundary_loss_term)))
train_loss = l2 + l3
train_loss.backward(retain_graph=True)
return train_loss.item()
loss_value = self.optimizer.step(closure)
if device_string == "cuda":
torch.cuda.synchronize() # second call right before time clock to finish all operations
epoch_time = time.perf_counter() - start
'''
logging errors and printing them
'''
training_pred = self.w.forward(self.X_tilde)
test_pred = self.w.forward(self.test_X_tilde)
# TRAINING
pred_tilde = self.w.forward(self.X_tilde)
u_x = grad(pred_tilde, self.x_tilde, grad_outputs=torch.ones_like(
pred_tilde), create_graph=True, retain_graph=True)[0]
u_xx = grad(u_x, self.x_tilde, grad_outputs=torch.ones_like(
pred_tilde), create_graph=True, retain_graph=True)[0]
u_y = grad(pred_tilde, self.y_tilde, grad_outputs=torch.ones_like(
pred_tilde), create_graph=True, retain_graph=True)[0]
u_yy = grad(u_y, self.y_tilde, grad_outputs=torch.ones_like(
pred_tilde), create_graph=True, retain_graph=True)[0]
# Poisson residual
pde_residual_training = (u_xx + u_yy) - self.f
boundary_pred = self.w.forward(self.X_b)
# first partial derivatives on the boundary
l2_w_x = grad(boundary_pred, self.x_b, grad_outputs=torch.ones_like(boundary_pred),
create_graph=True, retain_graph=True)[0]
l2_w_y = grad(boundary_pred, self.y_b, grad_outputs=torch.ones_like(boundary_pred),
create_graph=True, retain_graph=True)[0]
# combining the partial derivatives
w_xy = torch.hstack([l2_w_x, l2_w_y])
# element wise dot product between the normal vectors and first partial derivatives
gradient_n = torch.multiply(self.n, w_xy).sum(dim=1).unsqueeze(dim=1)
# loss on the boundary
boundary_residual_training = torch.multiply(self.alpha, gradient_n) + \
torch.multiply(self.beta, boundary_pred) - self.g
# TEST
pred_tilde_test = self.w.forward(self.test_X_tilde)
u_x = grad(pred_tilde_test, self.test_x_tilde, grad_outputs=torch.ones_like(
pred_tilde_test), create_graph=True, retain_graph=True)[0]
u_xx = grad(u_x, self.test_x_tilde, grad_outputs=torch.ones_like(
pred_tilde_test), create_graph=True, retain_graph=True)[0]
u_y = grad(pred_tilde_test, self.test_y_tilde, grad_outputs=torch.ones_like(
pred_tilde_test), create_graph=True, retain_graph=True)[0]
u_yy = grad(u_y, self.test_y_tilde, grad_outputs=torch.ones_like(
pred_tilde_test), create_graph=True, retain_graph=True)[0]
# Poisson residual
pde_residual_test = (u_xx + u_yy) - self.f_test
boundary_pred = self.w.forward(self.test_X_b)
# first partial derivatives on the boundary
l2_w_x = grad(boundary_pred, self.test_x_b, grad_outputs=torch.ones_like(boundary_pred),
create_graph=True, retain_graph=True)[0]
l2_w_y = grad(boundary_pred, self.test_y_b, grad_outputs=torch.ones_like(boundary_pred),
create_graph=True, retain_graph=True)[0]
# combining the partial derivatives
w_xy = torch.hstack([l2_w_x, l2_w_y])
# element wise dot product between the normal vectors and first partial derivatives
gradient_n = torch.multiply(self.n_test, w_xy).sum(dim=1).unsqueeze(dim=1)
# loss on the boundary
boundary_residual_test = torch.multiply(self.alpha_test, gradient_n) + \
torch.multiply(self.beta_test, boundary_pred) - self.g_test
# storing losses in variables
training_pde_residual = self.compute_linf(pde_residual_training)
test_pde_residual = self.compute_linf(pde_residual_test)
training_boundary_residual = self.compute_linf(boundary_residual_training)
test_boundary_residual = self.compute_linf(boundary_residual_test)
training_mse = self.compute_mse(training_pred, self.u_true)
test_mse = self.compute_mse(test_pred, self.test_u_true)
training_l2 = self.compute_l2(training_pred, self.u_true)
test_l2 = self.compute_l2(test_pred, self.test_u_true)
# logging losses and other important things in lists
self.logged_results['training_losses'].append(loss_value)
self.logged_results['training_mse_losses'].append(training_mse)
self.logged_results['training_l2_losses'].append(training_l2)
self.logged_results['training_pde_residual'].append(training_pde_residual)
self.logged_results['training_boundary_residual'].append(training_boundary_residual)
self.logged_results['test_mse_losses'].append(test_mse)
self.logged_results['test_l2_losses'].append(test_l2)
self.logged_results['test_pde_residual'].append(test_pde_residual)
self.logged_results['test_boundary_residual'].append(test_boundary_residual)
self.logged_results['epochs_list'].append(i)
self.logged_results['epoch_time'].append(epoch_time)
# Anneal learning rate if the loss is more than moving average of previous 10 elements
annealing_count = 0
annealing_counter = 0
if annealing_count > 10 and loss_value > sum(self.logged_results['training_losses'][-11:-1])/10.:
annealing_count = 0
annealing_counter += 1
print('\n' + '-'*40)
print('Annealing learning rate.')
self.optimizer.param_groups[0]['lr'] -= 0.025
print(f"New learning rate is: {self.optimizer.param_groups[0]['lr']}")
print('-'*40 + '\n')
annealing_count += 1
if i > 30 and (isnan(loss_value) or loss_value > 500):
# loss has exploded, this will trigger this run to restart
print(f"Loss exploded to: {loss_value}")
return False
if i % self.print_interval == 0 and self.verbosity:
print('='*70)
print(f'Iter {i},\nTraining loss = {loss_value}')
# laplacian(pinn) - f
print('\nLaplacian(pinn) - f')
print('===TRAINING' + '='*36)
print(training_pde_residual)
print('===TEST' + '='*40)
print(test_pde_residual)
# alpha * d/dn pinn + beta * pinn - g
print('\nalpha * d/dn pinn + beta * pinn - g')
print('===TRAINING' + '='*36)
print(training_boundary_residual)
print('===TEST' + '='*40)
print(test_boundary_residual)
# mse errors
print('\nMSE errors w.r.t. u_true')
# training
print('===TRAINING' + '='*36)
print(f'PINN MSE: {training_mse}')
# test
print('===TEST' + '='*40)
print(f'PINN MSE: {test_mse}')
# l2 errors
print(f'\nL2 errors w.r.t. u_true')
# training
print('===TRAINING' + '='*36)
print(f'PINN L2: {training_l2}')
# test
print('===TEST' + '='*40)
print(f'PINN L2: {test_l2}')
except KeyboardInterrupt:
print('Keyboard Interrupt. Ending training.')
return dict(self.logged_results)
print(f"Learning rate annealed {annealing_counter} times")
return dict(self.logged_results)
def save_results(data, file_name):
with open(file_name, 'w') as f:
json.dump(data, f, indent=4)
if __name__ == "__main__":
precision_strings = ["float32", "float64"]
orders = [2]
training_size = [582, 828, 1663, 2236, 3196, 4977, 6114, 8767, 19638]
supervised_options = [False]
activation_function = 'tanh'
lr = 0.2
for precision_string in precision_strings:
PRECISION = torch.float32 if precision_string == "float32" else torch.float64
results_folder = f"gpu_{precision_string}_synced_vanilla_results_noprint"
for cur_supervised_option in supervised_options:
print(f'\nGoing over supervised={cur_supervised_option}')
for order in orders:
for size in training_size:
supervised_file_bool = 'supervised' if cur_supervised_option else 'unsupervised'
file_name = f"{order}_{size}"
test_name = f"{order}_21748_test"
save_folder = f'../{results_folder}/vanilla_pinn/{order}/{size}/{supervised_file_bool}/'
if not os.path.isdir(save_folder):
os.makedirs(save_folder)
save_file_name = save_folder + 'results.json'
print('\n\n')
print('+'*70)
print(f'Running {precision_string} vanilla-PINN on {file_name} with {activation_function}')
print('+'*70)
print('\n\n')
# read mat files
X_i = torch.tensor(loadmat(f"../scai/files_{file_name}/Xi.mat")["Xi"], dtype=PRECISION, requires_grad=True).to(device)
X_b = torch.tensor(loadmat(f"../scai/files_{file_name}/Xb.mat")["Xb"], dtype=PRECISION, requires_grad=True).to(device)
X_g = torch.tensor(loadmat(f"../scai/files_{file_name}/Xg.mat")["X_g"], dtype=PRECISION, requires_grad=True).to(device)
n = torch.tensor(loadmat(f"../scai/files_{file_name}/n.mat")["n"], dtype=PRECISION, requires_grad=True).to(device)
u_true = torch.tensor(loadmat(f"../scai/files_{file_name}/u.mat")["u"], dtype=PRECISION).to(device)
f = torch.tensor(loadmat(f"../scai/files_{file_name}/f.mat")["f"], dtype=PRECISION, requires_grad=True).to(device)
g = torch.tensor(loadmat(f"../scai/files_{file_name}/g.mat")["g"], dtype=PRECISION, requires_grad=True).to(device)
alpha = torch.tensor(loadmat(f"../scai/files_{file_name}/alpha.mat")["Neucoeff"], dtype=PRECISION, requires_grad=True).to(device)
beta = torch.tensor(loadmat(f"../scai/files_{file_name}/beta.mat")["Dircoeff"], dtype=PRECISION, requires_grad=True).to(device)
b_starts = X_i.shape[0]
b_end = b_starts + X_b.shape[0]
# test files
X_i_test = torch.tensor(loadmat(f"../scai/files_{test_name}/Xi.mat")["Xi"], dtype=PRECISION, requires_grad=True).to(device)
X_b_test = torch.tensor(loadmat(f"../scai/files_{test_name}/Xb.mat")["Xb"], dtype=PRECISION, requires_grad=True).to(device)
test_u_true = torch.tensor(loadmat(f"../scai/files_{test_name}/u.mat")["u"], dtype=PRECISION).to(device)
f_test = torch.tensor(loadmat(f"../scai/files_{test_name}/f.mat")["f"], dtype=PRECISION, requires_grad=True).to(device)
g_test = torch.tensor(loadmat(f"../scai/files_{test_name}/g.mat")["g"], dtype=PRECISION, requires_grad=True).to(device)
alpha_test = torch.tensor(loadmat(f"../scai/files_{test_name}/alpha.mat")["Neucoeff"], dtype=PRECISION, requires_grad=True).to(device)
beta_test = torch.tensor(loadmat(f"../scai/files_{test_name}/beta.mat")["Dircoeff"], dtype=PRECISION, requires_grad=True).to(device)
n_test = torch.tensor(loadmat(f"../scai/files_{test_name}/n.mat")["n"], dtype=PRECISION, requires_grad=True).to(device)
test_x_i = X_i_test[:, 0].unsqueeze(dim=1)
test_y_i = X_i_test[:, 1].unsqueeze(dim=1)
test_x_b = X_b_test[:, 0].unsqueeze(dim=1)
test_y_b = X_b_test[:, 1].unsqueeze(dim=1)
test_x_tilde = torch.vstack([test_x_i, test_x_b])
test_y_tilde = torch.vstack([test_y_i, test_y_b])
test_X_tilde = torch.hstack([test_x_tilde, test_y_tilde])
test_X_b = torch.hstack([test_x_b, test_y_b])
# need to separate the spatial dimensions in X matrices for proper partial derivatives with autograd
x_i = X_i[:, 0].unsqueeze(dim=1)
y_i = X_i[:, 1].unsqueeze(dim=1)
x_b = X_b[:, 0].unsqueeze(dim=1)
y_b = X_b[:, 1].unsqueeze(dim=1)
x_g = X_g[:, 0].unsqueeze(dim=1)
y_g = X_g[:, 1].unsqueeze(dim=1)
# only compute losses on interior and boundary points
ib_idx = X_i.shape[0] + X_b.shape[0]
# define list for Trainer input
config = {
'spatial_dim': 2,
'precision': precision_string,
'activation': activation_function,
'order': 2, # activation order
'network_device': device_string,
'layers': 4,
'nodes': 50,
'epochs': 5000,
'optimizer': 'lbfgs',
'lr': lr,
}
print(f"Learning rate: {config['lr']}")
vars = {
'n': n,
'x_i': x_i,
'x_b': x_b,
'x_g': x_g,
'y_i': y_i,
'y_b': y_b,
'y_g': y_g,
'ib_idx': ib_idx,
'u_true': u_true,
'test_X_tilde': test_X_tilde,
'test_u_true': test_u_true,
'test_x_i': test_x_i,
'test_y_i': test_y_i,
'test_x_b': test_x_b,
'test_y_b': test_y_b,
'test_x_tilde': test_x_tilde,
'test_y_tilde': test_y_tilde,
'test_X_b': test_X_b,
'f_test': f_test,
'beta_test': beta_test,
'alpha_test': alpha_test,
'g_test': g_test,
'n_test': n_test,
'f': f,
'g': g,
'alpha': alpha,
'beta': beta,
'b_end': b_end,
'b_starts': b_starts,
'supervised': cur_supervised_option,
'print_interval': 10,
'verbosity': True,
}
flag = True
while flag:
trainer = Trainer(config=config, **vars)
logged_results = trainer.train()
if type(logged_results) == bool:
config['lr'] /= 2.0
print(f"Restarting with learning rate = {config['lr']}")
continue
else:
flag = False
logged_results = logged_results | config
save_results(logged_results, save_file_name)
config['lr'] = lr