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1d_wave_point_optimization.py
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import torch
import torch.nn as nn
import os
import matplotlib.pyplot as plt
import random
from torch.optim import LBFGS, Adam
from tqdm import tqdm
import argparse
from util import *
from model_dict import get_model
seed = 0
np.random.seed(seed)
random.seed(seed)
torch.manual_seed(seed)
torch.cuda.manual_seed(seed)
parser = argparse.ArgumentParser('Training Point Optimization')
parser.add_argument('--model', type=str, default='PINN')
parser.add_argument('--device', type=str, default='cuda:0')
args = parser.parse_args()
device = args.device
res, b_left, b_right, b_upper, b_lower = get_data([0, 1], [0, 1], 101, 101)
res_test, _, _, _, _ = get_data([0, 1], [0, 1], 101, 101)
if args.model == 'PINNsFormer' or args.model == 'PINNsFormer_Enc_Only':
res = make_time_sequence(res, num_step=5, step=1e-4)
b_left = make_time_sequence(b_left, num_step=5, step=1e-4)
b_right = make_time_sequence(b_right, num_step=5, step=1e-4)
b_upper = make_time_sequence(b_upper, num_step=5, step=1e-4)
b_lower = make_time_sequence(b_lower, num_step=5, step=1e-4)
res = torch.tensor(res, dtype=torch.float32, requires_grad=True).to(device)
b_left = torch.tensor(b_left, dtype=torch.float32, requires_grad=True).to(device)
b_right = torch.tensor(b_right, dtype=torch.float32, requires_grad=True).to(device)
b_upper = torch.tensor(b_upper, dtype=torch.float32, requires_grad=True).to(device)
b_lower = torch.tensor(b_lower, dtype=torch.float32, requires_grad=True).to(device)
x_res, t_res = res[:, ..., 0:1], res[:, ..., 1:2]
x_left, t_left = b_left[:, ..., 0:1], b_left[:, ..., 1:2]
x_right, t_right = b_right[:, ..., 0:1], b_right[:, ..., 1:2]
x_upper, t_upper = b_upper[:, ..., 0:1], b_upper[:, ..., 1:2]
x_lower, t_lower = b_lower[:, ..., 0:1], b_lower[:, ..., 1:2]
def init_weights(m):
if isinstance(m, nn.Linear):
torch.nn.init.xavier_uniform(m.weight)
m.bias.data.fill_(0.01)
if args.model == 'KAN':
model = get_model(args).Model(width=[2, 5, 5, 1], grid=5, k=3, grid_eps=1.0, \
noise_scale_base=0.25, device=device).to(device)
elif args.model == 'QRes':
model = get_model(args).Model(in_dim=2, hidden_dim=256, out_dim=1, num_layer=4).to(device)
model.apply(init_weights)
elif args.model == 'PINNsFormer' or args.model == 'PINNsFormer_Enc_Only':
model = get_model(args).Model(in_dim=2, hidden_dim=32, out_dim=1, num_layer=1).to(device)
model.apply(init_weights)
else:
model = get_model(args).Model(in_dim=2, hidden_dim=512, out_dim=1, num_layer=4).to(device)
model.apply(init_weights)
optim = LBFGS(model.parameters(), line_search_fn='strong_wolfe')
n_params = get_n_params(model)
print(model)
print(get_n_params(model))
loss_track = []
pi = torch.tensor(np.pi, dtype=torch.float32, requires_grad=False).to(device)
for i in tqdm(range(1000)):
def closure():
pred_res = model(x_res, t_res)
pred_left = model(x_left, t_left)
pred_right = model(x_right, t_right)
pred_upper = model(x_upper, t_upper)
pred_lower = model(x_lower, t_lower)
u_x = torch.autograd.grad(pred_res, x_res, grad_outputs=torch.ones_like(pred_res), retain_graph=True,
create_graph=True)[0]
u_xx = \
torch.autograd.grad(u_x, x_res, grad_outputs=torch.ones_like(pred_res), retain_graph=True,
create_graph=True)[0]
u_t = torch.autograd.grad(pred_res, t_res, grad_outputs=torch.ones_like(pred_res), retain_graph=True,
create_graph=True)[0]
u_tt = \
torch.autograd.grad(u_t, t_res, grad_outputs=torch.ones_like(pred_res), retain_graph=True,
create_graph=True)[0]
loss_res = torch.mean((u_tt - 4 * u_xx) ** 2)
loss_bc = torch.mean((pred_upper) ** 2) + torch.mean((pred_lower) ** 2)
ui_t = torch.autograd.grad(pred_left, t_left, grad_outputs=torch.ones_like(pred_left), retain_graph=True,
create_graph=True)[0]
loss_ic_1 = torch.mean(
(pred_left[:, 0] - torch.sin(pi * x_left[:, 0]) - 0.5 * torch.sin(3 * pi * x_left[:, 0])) ** 2)
loss_ic_2 = torch.mean((ui_t) ** 2)
loss_ic = loss_ic_1 + loss_ic_2
loss_track.append([loss_res.item(), loss_ic.item(), loss_bc.item()])
loss = loss_res + loss_ic + loss_bc
optim.zero_grad()
loss.backward()
return loss
optim.step(closure)
print('Loss Res: {:4f}, Loss_BC: {:4f}, Loss_IC: {:4f}'.format(loss_track[-1][0], loss_track[-1][1], loss_track[-1][2]))
print('Train Loss: {:4f}'.format(np.sum(loss_track[-1])))
if not os.path.exists('./results/'):
os.makedirs('./results/')
torch.save(model.state_dict(), f'./results/1dwave_{args.model}_point.pt')
# Visualize
if args.model == 'PINNsFormer' or args.model == 'PINNsFormer_Enc_Only':
res_test = make_time_sequence(res_test, num_step=5, step=1e-4)
res_test = torch.tensor(res_test, dtype=torch.float32, requires_grad=True).to(device)
x_test, t_test = res_test[:, ..., 0:1], res_test[:, ..., 1:2]
with torch.no_grad():
pred = model(x_test, t_test)[:, 0:1]
pred = pred.cpu().detach().numpy()
pred = pred.reshape(101, 101)
def u_ana(x, t):
return np.sin(np.pi * x) * np.cos(2 * np.pi * t) + 0.5 * np.sin(3 * np.pi * x) * np.cos(6 * np.pi * t)
res_test, _, _, _, _ = get_data([0, 1], [0, 1], 101, 101)
u = u_ana(res_test[:, 0], res_test[:, 1]).reshape(101, 101)
rl1 = np.sum(np.abs(u - pred)) / np.sum(np.abs(u))
rl2 = np.sqrt(np.sum((u - pred) ** 2) / np.sum(u ** 2))
print('relative L1 error: {:4f}'.format(rl1))
print('relative L2 error: {:4f}'.format(rl2))
plt.figure(figsize=(4, 3))
plt.imshow(pred, aspect='equal')
plt.xlabel('x')
plt.ylabel('t')
plt.title('Predicted u(x,t)')
plt.colorbar()
plt.tight_layout()
plt.axis('off')
plt.savefig(f'./results/1dreaction_{args.model}_point_optimization_pred.pdf', bbox_inches='tight')
plt.figure(figsize=(4, 3))
plt.imshow(u, aspect='equal')
plt.xlabel('x')
plt.ylabel('t')
plt.title('Exact u(x,t)')
plt.colorbar()
plt.tight_layout()
plt.axis('off')
plt.savefig('./results/1dreaction_exact.pdf', bbox_inches='tight')
plt.figure(figsize=(4, 3))
plt.imshow(pred - u, aspect='equal', cmap='coolwarm', vmin=-0.3, vmax=0.3)
plt.xlabel('x')
plt.ylabel('t')
plt.title('Absolute Error')
plt.colorbar()
plt.tight_layout()
plt.axis('off')
plt.savefig(f'./results/1dreaction_{args.model}_point_optimization_error.pdf', bbox_inches='tight')