weili101 / deep_plates Goto Github PK

Hello,

Thank you for providing the code for your paper, it has proven so so valuable in my own research.
Regarding the implementation of the ANN, in the paper you state that you train a single 5 layers deep 5 neurons wide net with two outputs (u and v respectively). However in the code provided (I'm looking at the open hole energy problem for example) there are two nets, one for u and one for v, each 10 layers deep and 20 neurons wide. This is significantly deeper and wider then what is discussed in the paper.
Am I understanding everything correctly and is there a reason for the discrepancy?

Again thank you so much,
Alexi

Hello, I've noticed that there are some operations involved when calculating both first-order and second-order derivatives in your Example 1 - Uniaxial tension, PDE-based problem. Could you please explain why these operations are necessary?

def PDE(x, Net_u, func_u, Net_v, func_v):

_, _, _, du_xx, du_yy, du_xy = derivative(x, Net_u, func_u, '2') 
_, _, _, dv_xx, dv_yy, dv_xy = derivative(x, Net_v, func_v, '2')

du_xx, du_yy, du_xy = du_xx/a, du_yy*a/b**2, du_xy/b
dv_xx, dv_yy, dv_xy = dv_xx*b/a**2, dv_yy/b, dv_xy/a

    Hello author, thank you very much for sharing the code.
    In the class for "derivative", my understanding is that Net(x) is the output of the neural network, which is the predictive value "w", so what does the function "func(x)" do?
    I already know the specific definition of "func(x)" in the following text, but I do not know the function of "func(x)" in the class of "derivative".
    Thanks!

def derivative(x, Net, func, order):

w = Net(x)*func(x).view(-1,1)                                #func(x)？？？？？？？？？？？？？？？？？

if order == '0':
    return w

else:
    dw_xy = torch.autograd.grad(w, x, torch.ones_like(w), 
                                retain_graph=True, create_graph=True, allow_unused=True)
    dw_x = dw_xy[0][:,0].view(-1,1)
    dw_y = dw_xy[0][:,1].view(-1,1)
    
    if order == '1':
        return w, dw_x, dw_y

    else:
        dw_xxy = torch.autograd.grad(dw_x, x, torch.ones_like(dw_x), 
                                     retain_graph=True, create_graph=True,allow_unused=True)
        dw_xx = dw_xxy[0][:,0].view(-1,1)
        dw_xy = dw_xxy[0][:,1].view(-1,1)
        dw_yy = torch.autograd.grad(dw_y, x, torch.ones_like(dw_y), retain_graph=True, 
                                    create_graph=True,allow_unused=True)[0][:,1].view(-1,1)
        return w, dw_x, dw_y, dw_xx, dw_yy, dw_xy

Dear Dr.Li
I am very happy to find your article,because it has inspired me a lot.But there are some questions I don't understand.In your section Ex1 Flat_tension_PDE_based_NN,if I want to change the boundary conditions，such as U=0andV=0（x=0) , what should I do.Forgive me for my stupidity,I cannot find the answer in code.

Looking forward to your reply.Please forgive me for any inconvenience.

Thanks for sharing the codes of the PDE-based PINN. However, I cannot understand why the derivatives need to multiply and divide the model size, like in the code for first order derivatives: du_y, dv_x = du_ya/b, dv_xb/a, and for second order derivatives: du_xx, du_yy, du_xy = du_xx/a, du_yy*a/b**2, du_xy/b. We're guessing that these are modifications for implicit derivatives. We sincerely invite your guidance, thank you!