PDE.py

'''
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

'''
Jac_Det ------------- Computes the Jacobian Determinant for the given input.

Parameters -------- x --------------------------------- input points
                    y --------------------------------- output of the network
                    func_g ---------------------------- Function g as specified in our formulation
                    constant -------------------------- normalisation constant for functions f and g
                    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.
                    flag ------------------------------ True -- diffeo given by gradient of network
                                                        False - diffeo given by x + grad(Network)
'''
def Jac_Det(y, x, func_g, constant, periodic_Boundary_Flag, flag=True):
    dy, = grad(y.sum(), x, create_graph=True, retain_graph=True)

    if periodic_Boundary_Flag:
        if flag:
            dy_2 = dy.clone()
            dy_2[:, 0] = Periodic_Cond(dy[:, 0], -3, 3)
            dy_2[:, 1] = Periodic_Cond(dy[:, 1], -3, 3)

            grad_u = dy_2
        else:
            dy_2 = dy.clone()
            dy_2[:, 0] = Periodic_Cond(x[:, 0] + dy[:, 0], -3, 3)
            dy_2[:, 1] = Periodic_Cond(x[:, 1] + dy[:, 1], -3, 3)

            x_grad_u = dy_2
    else:
        if flag:
            grad_u = dy
        else:
            x_grad_u = x + dy

    du_x, du_y = dy[:, 0], dy[:, 1]

    dy, = grad(du_x.sum(), x, create_graph=True, retain_graph=True)
    d2u_x, du_xy = dy[:, 0], dy[:, 1]

    dy, = grad(du_y.sum(), x, create_graph=True, retain_graph=True)
    d2u_y, du_yx = dy[:, 1], dy[:, 0]

    if flag:
        det_u = (d2u_x * d2u_y) - (du_xy * du_yx)
        g = func_g(grad_u, constant).squeeze()
    else:
        det_u = ((1 + d2u_x) * (1 + d2u_y)) - (du_xy * du_yx)
        g = func_g(x_grad_u, constant).squeeze()

    return g * det_u