-
-
Notifications
You must be signed in to change notification settings - Fork 3
/
Copy pathLoss_Function.py
129 lines (98 loc) · 7.03 KB
/
Loss_Function.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
'''
Copyright 2020 Amanpreet Singh,
Martin Bauer,
Sarang Joshi
Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
'''
import torch
from torch.autograd import grad
'''
KL_loss ------------- Computes the KL divergence loss for the given input. (This is for the discrete formulation)
Refer to Eq 7 in paper.
Parameters -------- x --------------------------------- input points
y --------------------------------- output of the network
flag ------------------------------ boundary flag for points
BC_error_func --------------------- Function to compute loss at the boundaries
func_f ---------------------------- Function f as specified in our formulation
func_g ---------------------------- Function g as specified in our formulation
constant -------------------------- normalisation constant for functions f and g
k --------------------------------- Not used here.
periodic_Boundary_Flag ------------ Flag to specify the if we want to impose boundary conditions on
input, i.e. to wrap around the points that go out of domain.
Note that this does not work well and should be kept as False.
add_boundary_loss_flag ------------ Flag if we want to add boundary loss in our loss function.
As pf now no boundary conditions are imposed.
Not even implemented.
deformation flag ------------------ True -------- diffeo given by x + grad(network)(Not mentioned in
Paper. Difficult to impose convexity with such a formulation)
False ------- diffeo given by grad(network)
'''
def KLLoss(x, y, flag, BC_error_func, func_f, func_g, constant, k, periodic_Boundary_Flag=False,
add_boundary_loss_flag=1, deformation_flag=False):
dy, = grad(y.sum(), x, create_graph=True, retain_graph=True)
# print("Gradient is NaN : ", (dy != dy).sum())
if deformation_flag:
dy_2 = x + dy
else:
dy_2 = dy
x_grad_u = dy_2
g_grad_u = func_g(x_grad_u, constant).squeeze()
der = torch.zeros((x.shape[0], x.shape[1], x.shape[1])).cuda()
for dim in range(x.shape[1]):
der[:, dim, :] = grad(dy[:, dim].sum(), x, create_graph=True, retain_graph=True)[0]
if deformation_flag:
I = torch.eye(x.shape[1])
I = I.reshape((1, x.shape[1], x.shape[1]))
I = I.repeat(x.shape[0], 1, 1).cuda()
det_Hu = torch.det(I + der)
else:
det_Hu = torch.det(der)
kl_loss = -(torch.log(det_Hu) + g_grad_u)#torch.log(g_grad_u))
if deformation_flag:
f_norm = torch.pow(der, 2).reshape(der.shape[0], der.shape[1]**2).sum(dim=-1)
else:
I = torch.eye(x.shape[1])
I = I.reshape((1, x.shape[1], x.shape[1]))
I = I.repeat(x.shape[0], 1, 1).cuda()
f_norm = torch.pow(I - der, 2).reshape(der.shape[0], der.shape[1]**2).sum(dim=-1)
kl_loss = kl_loss + k*f_norm
return kl_loss.unsqueeze(-1)
'''
Hess_loss ------------- Loss function to train a network such that grad(u) = x
Parameters -------- x --------------------------------- input points
y --------------------------------- output of the network
flag ------------------------------ boundary flag for points
BC_error_func --------------------- Function to compute loss at the boundaries
func_f ---------------------------- Function f as specified in our formulation
func_g ---------------------------- Function g as specified in our formulation
constant -------------------------- normalisation constant for functions f and g
k --------------------------------- Not used here.
periodic_Boundary_Flag ------------ Flag to specify the if we want to impose boundary conditions on
input, i.e. to wrap around the points that go out of domain.
Note that this does not work well and should be kept as False.
add_boundary_loss_flag ------------ Flag if we want to add boundary loss in our loss function.
As pf now no boundary conditions are imposed.
Not even implemented.
deformation flag ------------------ True -------- diffeo given by x + grad(network)(Not mentioned in
Paper. Difficult to impose convexity with such a formulation)
False ------- diffeo given by grad(network)
Most parameters are ignored. Are provided just to ensure we can use the same training code across
all experiments.
'''
def HessLoss(x, y, flag, BC_error_func, func_f, func_g, constant, k, periodic_Boundary_Flag, add_boundary_loss_flag=1,
deformation_flag=False):
dy, = grad(y.sum(), x, create_graph=True, retain_graph=True)
loss = torch.zeros_like(x[:, 0])
for dim in range(x.shape[1]):
loss = loss + torch.abs(dy[:, dim] - x[:, dim])
return loss.unsqueeze(-1)
'''
IdentityLoss --- returns the mean of outputs as loss
Parameters -------- outputs -- output of network
targets -- not used here
'''
def IdentityLoss(outputs, targets):
return outputs.sum()/outputs.shape[0]