JinshuaiBai
commented
11 months ago Thank you for your nice words.
- Dif_op_u and Dif_op_v are the functions to calculate the derivatives of displacement u and v, respectively. Recall the pure bending beam case, the left boundary needs to satisfy that u(x=0)=0. In this case, we apply the hard boundary condition technique in PINN; that is, we let the output of FNN as intermediate output and multiply it with x ( u=FNN(x,y)*x ). By doing so, the boundary condition u(x=0)=0 can be naturally satisfied without introducing additional loss terms to impose this condition. It is worth highlighting that the training process will be more challenging (harder to converge) if more loss terms are introduced. On the other hand, the displacement v doesn't need to satisfy any hard boundary condition. Therefore, the U=temp is directly applied without multiplying x or y.
- The list y is not the output of the PINN, they are ground truths of the problem; that is, the traction boundary conditions of the pure bending beam. Those data are known before training, and they are used to correct the stress boundary condition predictions from the PINN. You can refer to basic elastic mechanics books for more details.
Hope this can answer your questions.
Biyhjj
jackliuzefeng
Dear Dr.Bai
I would like to say the idea behind your work is impressive!And i am trying to predict the U and V according to 01_pure_bend you have introduced.But I am confused about a few points.
Thanks for replying