├── .idea
    ├── DeepBSDE-pytorch.iml
    ├── inspectionProfiles
    │   └── Project_Default.xml
    ├── modules.xml
    ├── vcs.xml
    └── workspace.xml
├── AllenCahn_training_history.csv
├── README.md
├── config.py
├── equation.py
├── solver.py
└── train.py


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/AllenCahn_training_history.csv:
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 1 | step,loss_function,target_value,elapsed_time
 2 | 0,5.39418e-02,3.26080e-01,0
 3 | 100,3.44411e-02,2.78099e-01,13
 4 | 200,2.31878e-02,2.35126e-01,26
 5 | 300,1.58378e-02,1.97588e-01,39
 6 | 400,9.66999e-03,1.65539e-01,52
 7 | 500,6.76427e-03,1.38360e-01,65
 8 | 600,6.04422e-03,1.15831e-01,78
 9 | 700,4.32909e-03,9.79632e-02,92
10 | 800,4.50971e-03,8.42173e-02,105
11 | 900,3.48606e-03,7.42119e-02,118
12 | 1000,3.63141e-03,6.66798e-02,131
13 | 1100,3.00041e-03,6.09193e-02,144
14 | 1200,3.87503e-03,5.73990e-02,157
15 | 1300,2.88035e-03,5.50455e-02,170
16 | 1400,3.58197e-03,5.41830e-02,183
17 | 1500,3.43098e-03,5.44178e-02,196
18 | 1600,3.31472e-03,5.32332e-02,209
19 | 1700,3.04519e-03,5.22913e-02,223
20 | 1800,3.61448e-03,5.29079e-02,236
21 | 1900,4.06360e-03,5.27411e-02,249
22 | 2000,2.80823e-03,5.29730e-02,262
23 | 2100,3.39954e-03,5.13978e-02,275
24 | 2200,3.80409e-03,5.22298e-02,288
25 | 2300,4.08157e-03,5.20794e-02,301
26 | 2400,3.93781e-03,5.21230e-02,315
27 | 2500,3.23211e-03,5.20974e-02,328
28 | 2600,3.28405e-03,5.37664e-02,342
29 | 2700,3.89592e-03,5.27176e-02,355
30 | 2800,3.16535e-03,5.19796e-02,368
31 | 2900,3.55510e-03,5.14435e-02,382
32 | 3000,3.41030e-03,5.23272e-02,395
33 | 3100,3.02276e-03,5.29629e-02,409
34 | 3200,4.09172e-03,5.16499e-02,422
35 | 3300,3.32843e-03,5.28555e-02,435
36 | 3400,3.21832e-03,5.10399e-02,448
37 | 3500,3.13571e-03,5.17579e-02,461
38 | 3600,3.32771e-03,5.34426e-02,475
39 | 3700,3.44333e-03,5.26195e-02,488
40 | 3800,3.02391e-03,5.36960e-02,502
41 | 3900,3.37896e-03,5.22397e-02,515
42 | 4000,3.35890e-03,5.15655e-02,528
43 | 


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/README.md:
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1 | Reproduce "Solving high-dimensional partial differential equations using deep learning" by pytorch


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/config.py:
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 1 | import numpy as np
 2 | 
 3 | 
 4 | class Config(object):
 5 |     n_layer = 4
 6 |     batch_size = 64
 7 |     valid_size = 256
 8 |     step_boundaries = [2000, 4000]
 9 |     num_iterations = 6000
10 |     logging_frequency = 100
11 |     verbose = True
12 |     y_init_range = [0, 1]
13 | 
14 | 
15 | class AllenCahnConfig(Config):
16 |     total_time = 0.3
17 |     num_time_interval = 20
18 |     dim = 100
19 |     lr_values = list(np.array([5e-4, 5e-4]))
20 |     lr_boundaries = [2000]
21 |     num_iterations = 4000
22 |     num_hiddens = [dim, dim + 10, dim + 10, dim]
23 |     y_init_range = [0.3, 0.6]
24 | 
25 | 
26 | class HJBConfig(Config):
27 |     # Y_0 is about 4.5901.
28 |     dim = 100
29 |     total_time = 1.0
30 |     num_time_interval = 20
31 |     lr_boundaries = [400]
32 |     num_iterations = 2000
33 |     lr_values = list(np.array([1e-2, 1e-2]))
34 |     num_hiddens = [dim, dim+10, dim+10, dim]
35 |     y_init_range = [0, 1]
36 | 
37 | 
38 | class PricingOptionConfig(Config):
39 |     dim = 100
40 |     total_time = 0.5
41 |     num_time_interval = 20
42 |     lr_values = list(np.array([5e-3, 5e-3]))
43 |     lr_boundaries = [2000]
44 |     num_iterations = 4000
45 |     num_hiddens = [dim, dim+10, dim+10, dim]
46 |     y_init_range = [15, 18]
47 | 
48 | 
49 | class PricingDefaultRiskConfig(Config):
50 |     dim = 100
51 |     total_time = 1
52 |     num_time_interval = 40
53 |     lr_values = list(np.array([8e-3, 8e-3]))
54 |     lr_boundaries = [3000]
55 |     num_iterations = 6000
56 |     num_hiddens = [dim, dim+10, dim+10, dim]
57 |     y_init_range = [40, 50]
58 | 
59 | 
60 | class BurgesTypeConfig(Config):
61 |     dim = 50
62 |     total_time = 0.2
63 |     num_time_interval = 30
64 |     lr_values = list(np.array([1e-2, 1e-3, 1e-4]))
65 |     lr_boundaries = [15000, 25000]
66 |     num_iterations = 30000
67 |     num_hiddens = [dim, dim+10, dim+10, dim]
68 |     y_init_range = [2, 4]
69 | 
70 | 
71 | class QuadraticGradientsConfig(Config):
72 |     dim = 100
73 |     total_time = 1.0
74 |     num_time_interval = 30
75 |     lr_values = list(np.array([5e-3, 5e-3]))
76 |     lr_boundaries = [2000]
77 |     num_iterations = 4000
78 |     num_hiddens = [dim, dim+10, dim+10, dim]
79 |     y_init_range = [2, 4]
80 | 
81 | 
82 | class ReactionDiffusionConfig(Config):
83 |     dim = 100
84 |     total_time = 1.0
85 |     num_time_interval = 30
86 |     lr_values = list(np.array([1e-2, 1e-2, 1e-2]))
87 |     lr_boundaries = [8000, 16000]
88 |     num_iterations = 24000
89 |     num_hiddens = [dim, dim+10, dim+10, dim]
90 | 
91 | 
92 | def get_config(name):
93 |     try:
94 |         return globals()[name+'Config']
95 |     except KeyError:
96 |         raise KeyError("Config for the required problem not found.")
97 | 


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/equation.py:
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 1 | import numpy as np
 2 | import torch
 3 | from scipy.stats import multivariate_normal as normal
 4 | 
 5 | 
 6 | class Equation(object):
 7 |     """Base class for defining PDE related function."""
 8 | 
 9 |     def __init__(self, dim, total_time, num_time_interval):
10 |         self._dim = dim
11 |         self._total_time = total_time
12 |         self._num_time_interval = num_time_interval
13 |         self._delta_t = (self._total_time + 0.0) / self._num_time_interval
14 |         self._sqrt_delta_t = np.sqrt(self._delta_t)
15 |         self._y_init = None
16 | 
17 |     def sample(self, num_sample):
18 |         """Sample forward SDE."""
19 |         raise NotImplementedError
20 | 
21 |     def f_th(self, t, x, y, z):
22 |         """Generator function in the PDE."""
23 |         raise NotImplementedError
24 | 
25 |     def g_th(self, t, x):
26 |         """Terminal condition of the PDE."""
27 |         raise NotImplementedError
28 | 
29 |     @property
30 |     def y_init(self):
31 |         return self._y_init
32 | 
33 |     @property
34 |     def dim(self):
35 |         return self._dim
36 | 
37 |     @property
38 |     def num_time_interval(self):
39 |         return self._num_time_interval
40 | 
41 |     @property
42 |     def total_time(self):
43 |         return self._total_time
44 | 
45 |     @property
46 |     def delta_t(self):
47 |         return self._delta_t
48 | 
49 | 
50 | def get_equation(name, dim, total_time, num_time_interval):
51 |     try:
52 |         return globals()[name](dim, total_time, num_time_interval)
53 |     except KeyError:
54 |         raise KeyError("Equation for the required problem not found.")
55 | 
56 | 
57 | class AllenCahn(Equation):
58 |     def __init__(self, dim, total_time, num_time_interval):
59 |         super(AllenCahn, self).__init__(dim, total_time, num_time_interval)
60 |         self._x_init = np.zeros(self._dim)
61 |         self._sigma = np.sqrt(2.0)
62 | 
63 |     def sample(self, num_sample):
64 |         dw_sample = normal.rvs(size=[num_sample,
65 |                                      self._dim,
66 |                                      self._num_time_interval]) * self._sqrt_delta_t
67 |         x_sample = np.zeros([num_sample, self._dim, self._num_time_interval + 1])
68 |         x_sample[:, :, 0] = np.ones([num_sample, self._dim]) * self._x_init
69 |         for i in range(self._num_time_interval):
70 |             x_sample[:, :, i + 1] = x_sample[:, :, i] + self._sigma * dw_sample[:, :, i]
71 |         return torch.FloatTensor(dw_sample), torch.FloatTensor(x_sample)
72 | 
73 |     def f_th(self, t, x, y, z):
74 |         return y - torch.pow(y, 3)
75 | 
76 |     def g_th(self, t, x):
77 |         return 0.5 / (1 + 0.2 * torch.sum(x**2, dim=1, keepdim=True))
78 | 
79 | 
80 | 


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/solver.py:
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  1 | import numpy as np
  2 | import torch
  3 | import torch.nn as nn
  4 | import torch.nn.functional as F
  5 | from torch.nn import Parameter
  6 | 
  7 | TH_DTYPE = torch.float32
  8 | 
  9 | MOMENTUM = 0.99
 10 | EPSILON = 1e-6
 11 | DELTA_CLIP = 50.0
 12 | 
 13 | class Dense(nn.Module):
 14 | 
 15 |     def __init__(self,cin,cout, batch_norm=True, activate=True):
 16 |         super(Dense, self).__init__()
 17 |         self.cout = cout
 18 |         self.linear = nn.Linear(cin, cout)
 19 |         self.activate = activate
 20 |         if batch_norm:
 21 |             self.bn = nn.BatchNorm1d(cout,eps=EPSILON, momentum=MOMENTUM)
 22 |         else:
 23 |             self.bn = None
 24 |         nn.init.normal_(self.linear.weight,std=5.0/np.sqrt(cin+cout))
 25 | 
 26 |     def forward(self,x):
 27 |         x = self.linear(x)
 28 |         if self.bn is not None:
 29 |             x = self.bn(x)
 30 |         if self.activate:
 31 |             x = F.relu(x)
 32 |         return x
 33 | 
 34 | 
 35 | class Subnetwork(nn.Module):
 36 | 
 37 |     def __init__(self, config):
 38 |         super(Subnetwork, self).__init__()
 39 |         self._config = config
 40 |         self.bn = nn.BatchNorm1d(config.dim,eps=EPSILON, momentum=MOMENTUM)
 41 |         self.layers = [Dense(config.num_hiddens[i-1], config.num_hiddens[i]) for i in range(1, len(config.num_hiddens)-1)]
 42 |         self.layers += [Dense(config.num_hiddens[-2], config.num_hiddens[-1], activate=False)]
 43 |         self.layers = nn.Sequential(*self.layers)
 44 | 
 45 |     def forward(self,x):
 46 |         x = self.bn(x)
 47 |         x = self.layers(x)
 48 |         return x
 49 | 
 50 | 
 51 | 
 52 | class FeedForwardModel(nn.Module):
 53 |     """The fully connected neural network model."""
 54 |     def __init__(self, config, bsde):
 55 |         super(FeedForwardModel, self).__init__()
 56 |         self._config = config
 57 |         self._bsde = bsde
 58 | 
 59 |         # make sure consistent with FBSDE equation
 60 |         self._dim = bsde.dim
 61 |         self._num_time_interval = bsde.num_time_interval
 62 |         self._total_time = bsde.total_time
 63 | 
 64 |         self._y_init = Parameter(torch.Tensor([1]))
 65 |         self._y_init.data.uniform_(self._config.y_init_range[0], self._config.y_init_range[1])
 66 |         self._subnetworkList =nn.ModuleList([Subnetwork(config) for _ in range(self._num_time_interval-1)])
 67 | 
 68 | 
 69 |     def forward(self, x, dw):
 70 | 
 71 |         time_stamp = np.arange(0, self._bsde.num_time_interval) * self._bsde.delta_t
 72 | 
 73 |         z_init = torch.zeros([1, self._dim]).uniform_(-.1, .1).to(TH_DTYPE).cuda()
 74 | 
 75 |         all_one_vec = torch.ones((dw.shape[0], 1), dtype=TH_DTYPE).cuda()
 76 |         y = all_one_vec * self._y_init
 77 | 
 78 |         z = torch.matmul(all_one_vec, z_init)
 79 | 
 80 |         for t in range(0, self._num_time_interval-1):
 81 |             #print('y qian', y.max())
 82 |             y = y - self._bsde.delta_t * (
 83 |                 self._bsde.f_th(time_stamp[t], x[:, :, t], y, z)
 84 |                 )
 85 |             #print('y hou', y.max())
 86 |             add = torch.sum(z * dw[:, :, t], dim=1, keepdim=True)
 87 |             #print('add', add.max())
 88 |             y = y + add
 89 |             z = self._subnetworkList[t](x[:, :, t + 1]) / self._dim
 90 |             #print('z value', z.max())
 91 |         # terminal time
 92 |         y = y - self._bsde.delta_t * self._bsde.f_th(\
 93 |                     time_stamp[-1], x[:, :, -2], y, z\
 94 |                     ) + torch.sum(z * dw[:, :, -1], dim=1, keepdim=True)
 95 | 
 96 |         delta = y - self._bsde.g_th(self._total_time, x[:, :, -1])
 97 | 
 98 |         # use linear approximation outside the clipped range
 99 |         loss = torch.mean(torch.where(torch.abs(delta) < DELTA_CLIP, delta**2,
100 |                                                     2 * DELTA_CLIP * torch.abs(delta) - DELTA_CLIP ** 2))
101 |         return loss, self._y_init
102 | 
103 | 
104 | 
105 | 
106 | 


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/train.py:
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 1 | import time
 2 | from torchImpl.solver import FeedForwardModel
 3 | import logging
 4 | import torch.optim as optim
 5 | import numpy as np
 6 | import os
 7 | import torch
 8 | os.environ["CUDA_VISIBLE_DEVICES"]="1"
 9 | torch.backends.cudnn.benchmark=True
10 | 
11 | def train(config,bsde):
12 |     logging.basicConfig(level=logging.INFO,
13 |                         format='%(levelname)-6s %(message)s')
14 |     if bsde.y_init:
15 |         logging.info('Y0_true: %.4e' % bsde.y_init)
16 | 
17 |     # build and train
18 |     net = FeedForwardModel(config,bsde)
19 |     net.cuda()
20 | 
21 |     optimizer = optim.SGD(net.parameters(),5e-4)
22 |     start_time = time.time()
23 |     # to save iteration results
24 |     training_history = []
25 |     # for validation
26 |     dw_valid, x_valid = bsde.sample(config.valid_size)
27 | 
28 |     # begin sgd iteration
29 |     for step in range(config.num_iterations + 1):
30 |         if step % config.logging_frequency == 0:
31 |             net.eval()
32 |             loss, init = net(x_valid.cuda(), dw_valid.cuda())
33 | 
34 |             elapsed_time = time.time() - start_time
35 |             training_history.append([step, loss, init.item(), elapsed_time])
36 |             if config.verbose:
37 |                 logging.info("step: %5u,    loss: %.4e,   Y0: %.4e,  elapsed time %3u" % (
38 |                     step, loss, init.item(), elapsed_time))
39 | 
40 |         dw_train, x_train = bsde.sample(config.batch_size)
41 |         optimizer.zero_grad()
42 |         net.train()
43 |         loss, _ = net(x_train.cuda(), dw_train.cuda())
44 |         loss.backward()
45 | 
46 |         optimizer.step()
47 | 
48 |     training_history =np.array(training_history)
49 | 
50 |     if bsde.y_init:
51 |         logging.info('relative error of Y0: %s',
52 |                      '{:.2%}'.format(
53 |                          abs(bsde.y_init - training_history[-1, 2]) / bsde.y_init))
54 | 
55 | 
56 |     np.savetxt('{}_training_history.csv'.format(bsde.__class__.__name__),
57 |                 training_history,
58 |                 fmt=['%d', '%.5e', '%.5e', '%d'],
59 |                 delimiter=",",
60 |                 header="step,loss_function,target_value,elapsed_time",
61 |                 comments='')
62 | 
63 | if __name__ == '__main__':
64 |     from torchImpl.config import get_config
65 |     from torchImpl.equation import get_equation
66 |     cfg = get_config('AllenCahn')
67 |     bsde = get_equation('AllenCahn', cfg.dim, cfg.total_time, cfg.num_time_interval)
68 |     train(cfg,bsde)


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