Applying DeepONet to geotechnics

[dimasbetioli]

Dear colleagues

I am trying to apply DeepONet to geotechnical problems. I am first trying a 2D cylindrical deep tunnel in a layered space using the Mohr-Coulomb failure model. The input function is the shear modulus of the layers (G1, G2, ..., G10).

I used the Antiderivative operator from an aligned dataset (https://deepxde.readthedocs.io/en/latest/demos/operator/antiderivative_aligned.html) as a model to produce the code:

"""Backend supported: tensorflow.compat.v1"""
import deepxde as dde
import matplotlib.pyplot as plt
import numpy as np

Load dataset

d = np.load(r"C:\Users\dimas\OneDrive\Área de Trabalho\Files_NO\train.npz", allow_pickle=True)
X_train = (d["X_0"].astype(np.float32), d["X_1"].astype(np.float32))
y_train = d["y"].astype(np.float32)
d = np.load(r"C:\Users\dimas\OneDrive\Área de Trabalho\Files_NO\test.npz", allow_pickle=True)
X_test = (d["X_0"].astype(np.float32), d["X_1"].astype(np.float32))
y_test = d["y"].astype(np.float32)

data = dde.data.TripleCartesianProd(
X_train=X_train, y_train=y_train, X_test=X_test, y_test=y_test
)

Choose a network

m = 10
dim_x = 2
net = dde.nn.DeepONetCartesianProd(
[m, 40, 40],
[dim_x, 40, 40],
"relu",
"Glorot normal",
)

Define a Model

model = dde.Model(data, net)

Compile and Train

model.compile("adam", lr=0.001, metrics=["mean l2 relative error"])
losshistory, train_state = model.train(iterations=10000)

Plot the loss trajectory

dde.utils.plot_loss_history(losshistory)
plt.show()

The load is an initial condition with sxx = 30 MPa and syy = 30 MPa. The shear modulus of the layers is randomly generated, and the output is the displacement field in the x direction.

The code is running, but I cannot reach convergence. Would you have any tips for me?