Reynolds equation over a 2D disk domain with multiple hole

[Steph-Yhf]

model is as follows:
image

`import deepxde as dde
import matplotlib.pyplot as plt
from scipy.interpolate import griddata
import numpy as np
from deepxde.backend import torch

dde.config.set_random_seed(48)
dde.config.set_default_float('float64')

#parameter
h_thick=0.008
C=1
Pa=0
Ps=0.25
r_bearing = 30
r_hole = 0.1

#pde
def pde(x,y):
dp_xx = dde.grad.hessian(y, x, i=0, j=0)
dp_yy = dde.grad.hessian(y, x, i=1, j=1)
reynolds= dp_xx + dp_yy
return reynolds

#modeling
center=[0,0]
center1=[15,0]
center2=[0,15]
center3=[-15,0]
center4=[0,-15]
radius=r_bearing
radius_hole=r_hole
radius_points=1
inside_circle = dde.geometry.Disk(center, 10)
outer=dde.geometry.Disk(center, radius)
inner1=dde.geometry.Disk(center1, radius_hole)
innera= dde.geometry.Disk(center1, radius_points)
inner2=dde.geometry.Disk(center2, radius_hole)
innerb= dde.geometry.Disk(center2, radius_points)
inner3=dde.geometry.Disk(center3, radius_hole)
innerc= dde.geometry.Disk(center3, radius_points)
inner4=dde.geometry.Disk(center4, radius_hole)
innerd= dde.geometry.Disk(center4, radius_points)

def boundary(_, on_boundary):
return on_boundary

def boundary_outer(x, on_boundary):
return on_boundary and outer.on_boundary(x)

def boundary_inner1(x, on_boundary):
return on_boundary and inner1.on_boundary(x)

def boundary_inner2(x, on_boundary):
return on_boundary and inner2.on_boundary(x)

def boundary_inner3(x, on_boundary):
return on_boundary and inner3.on_boundary(x)

def boundary_inner4(x, on_boundary):
return on_boundary and inner4.on_boundary(x)

def funPs(x):
return Ps
def funPa(x):
return Pa
geom=outer - inner1 -inner2 - inner3 - inner4

outer_points = outer.uniform_boundary_points(2000)
inner1_points = inner1.random_boundary_points(0)
inner1_dom = inner1.uniform_points(12)
inner2_points = inner2.random_boundary_points(0)
inner2_dom = inner2.uniform_points(12)
inner3_points = inner3.random_boundary_points(0)
inner3_dom = inner3.uniform_points(12)
inner4_points = inner4.random_boundary_points(0)
inner4_dom = inner4.uniform_points(12)
innera_dom = innera.uniform_points(100)
innerb_dom = innerb.uniform_points(100)
innerc_dom = innerc.uniform_points(100)
innerd_dom = innerd.uniform_points(100)

points = np.append(inner1_points , inner1_dom , axis = 0)
points = np.append(points, inner2_points , axis=0)
points = np.append(points,inner2_dom , axis = 0)
points = np.append(points , inner3_points , axis = 0)
points = np.append(points,inner3_dom , axis = 0)
points = np.append(points , inner4_points , axis = 0)
points = np.append(points , inner4_dom , axis = 0)
points = np.append(points , innera_dom , axis = 0)
points = np.append(points , innerb_dom , axis = 0)
points = np.append(points , innerc_dom , axis = 0)
points = np.append(points , innerd_dom , axis = 0)
points = np.append(points , outer_points,axis = 0)

bc_in1 = dde.icbc.DirichletBC(inner1, funPs, boundary_inner1)
bc_in2 = dde.icbc.DirichletBC(inner2, funPs, boundary_inner2)
bc_in3 = dde.icbc.DirichletBC(inner3, funPs, boundary_inner3)
bc_in4 = dde.icbc.DirichletBC(inner4, funPs, boundary_inner4)
bc_out = dde.icbc.DirichletBC(outer, funPa, boundary_outer)
bcs= [bc_out, bc_in1, bc_in2, bc_in3, bc_in4]

data = dde.data.PDE(
geom,
pde,
bcs,
num_domain=5000,
num_boundary=200,
num_test=8000,
anchors= points
)

plt.figure(figsize = (32, 18))
plt.scatter(data.train_x_all[:,0], data.train_x_all[:,1], s = 0.3)
plt.axis('equal')

dde.config.set_default_float('float64')

layer_size = [2] +3* [50] + [1]
activation = 'tanh'
initializer = 'Glorot uniform'

net = dde.nn.FNN(layer_size, activation, initializer)
model = dde.Model(data, net)
loss_weights=[1, 1, 5, 5, 5, 5]

model.compile(
"adam",
lr=1e-3,
loss_weights=loss_weights
)

checkpointer=dde.callbacks.ModelCheckpoint(
"model/model", save_better_only=True, period=1000)
#model.compile("L-BFGS")
losshistory, train_state = model.train(iterations=5000,
display_every = 1000,
model_restore_path="model/model-4000.pt",
callbacks=[checkpointer]
)
dde.saveplot(losshistory, train_state, issave=True, isplot=True)`

Uploading image.png…
Question
Although train loss = 10e-5 and test loss = 10e-5, the result (the second picture) is wrong)
Please tell me what should I do, thanks?
I wonder if DEEPXDE can solve this problem