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Create a network geometry
Discussed in https://github.com/lululxvi/deepxde/discussions/1500
Originally posted by DeepaMahm September 27, 2023 Dear All,
I would like to create a network geometry (3D) in Deepxde to set up a diffusion problem.
I looked for the geometry creation options given in the documentation and I think I may need to use PointCloud.
I've used vedo in the past to create pointcloud
import networkx as nx
from vedo import *
G = nx.gnm_random_graph(n=30, m=55, seed=1)
nxpos = nx.spring_layout(G, dim=3)
nxpts = [nxpos[pt] for pt in sorted(nxpos)]
# node values
vals = list(range(10, 10+len(nxpts)))
nx_lines= []
for i, j in G.edges():
nx_lines.append([nxpos[i], nxpos[j]])
nx_pts = Points(nxpts, r=12)
nx_edg = Lines(nx_lines).lw(2)
Basically, I have the coordinates of the nodes in the geometry and Lines in vedo is used to define the edge connectivity i.e. the edge between two nodes.
Points in vedo would result in a pointcloud which I can pass to the class Geometry in Deepxde. I am a bit unsure if this is the right way tot proceed. And it is not clear to me how the lines have to be defined in Deepxde.
Suggestions on how to proceed would be of great help. Thanks so much for the amazing library.
Hi Prof. @lululxvi ,
If I interpolate and obtain the coordinates of points lying on the edge formed between 2 nodes, can these corrdinates be specified in the pointcloud geometry class to get the final network geometry?
Could someone please give me suggestions? I am not sure how to define a line object.
Hey, PINNs are meshless. This means you don't need lines, surfaces , planes etc. Just pass your the nodal coordinates as anchors. Here is an example,
data = dde.data.PDE(
geom,
pde,
[observed], # BCs
num_domain = 0,
num_boundary = 0,
anchors=nodes # collocation points
)
You just plug your collocation points i.e. the nodal coordinates as nodes and BC coordinates and its value as [observed]. You can define observed as follows:
observed = dde.icbc.PointSetBC(boundary_nodal_coordinates, boundary_solution)
Hi @praksharma ,
Thanks a lot. If I may ask another question,
To solve 1D diffusion problem, I tried to define Dirichlet boundary (value of 5) on the left and Neumann boundary on the right (zero gradient)
import deepxde as dde
import numpy as np
def pde(x, y):
"""
:param x: 2-dimensional vector; x[:, 0:1] = x-coordinate; x[:, 1:] = t-coordinate
:param y: network output; i.e., solution y(x,t)
:return:
"""
dc_t = dde.grad.jacobian(y, x, i=0, j=1)
dc_xx = dde.grad.hessian(y, x, i=0, j=0)
d = 1
return (
dc_t
- d * dc_xx
)
def boundary_l(x, on_boundary):
"""
Because of rounding-off errors, dde.utils.isclose(x[0], 0)
:param x:
:param on_boundary: all boundary points
:return:
"""
return on_boundary and dde.utils.isclose(x[0], 0)
def boundary_r(x, on_boundary):
"""
Because of rounding-off errors, dde.utils.isclose(x[0], 0)
:param x:
:param on_boundary: all boundary points
:return:
"""
return on_boundary and dde.utils.isclose(x[0], 1)
if __name__ == '__main__':
geom = dde.geometry.Interval(0, 1)
timedomain = dde.geometry.TimeDomain(0, 1)
geomtime = dde.geometry.GeometryXTime(geom, timedomain)
bc_l = dde.icbc.DirichletBC(geom, lambda x: 5, lambda _, on_boundary: boundary_l)
bc_r = dde.icbc.NeumannBC(geom, lambda x: 0, lambda _, on_boundary: boundary_r)
ic = dde.icbc.IC(geomtime, lambda x: 1, lambda _, on_initial: on_initial)
data = dde.data.TimePDE(
geomtime,
pde,
[bc_l, bc_r, ic],
num_domain=40, # no. of training residual points sampled inside the domain
num_boundary=20, # no. of training points sampled on the boundary
num_initial=10, # initial residual points for initial conditions
# solution=func, # reference solution to compute error of the dde solution, can be ignored if no exact soln
num_test=10000, # points for testing the residual
)
layer_size = [2] + [32] * 3 + [1] # width 32, depth 3
activation = "tanh"
initializer = "Glorot uniform"
net = dde.nn.FNN(layer_size, activation, initializer)
model = dde.Model(data, net)
model.compile("adam", lr=0.001, metrics=["l2 relative error"])
losshistory, train_state = model.train(iterations=10)
dde.saveplot(losshistory, train_state, issave=True, isplot=True)
I get the following error
return X[self.on_boundary(X, self.geom.on_boundary(X))]
~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
IndexError: arrays used as indices must be of integer (or boolean) type
I'm not sure how to fix this error.
Could you please have a look the boundary conditions? I'm not sure what's wrong.
bc_l = dde.icbc.DirichletBC(geom, lambda x: 5, lambda _, on_boundary: boundary_l)
bc_r = dde.icbc.NeumannBC(geom, lambda x: 0, lambda _, on_boundary: boundary_r)
The error is pretty obvious. You are using function within function. Try this.
bc_l = dde.icbc.DirichletBC(geom, lambda x: 5, boundary_l)
bc_r = dde.icbc.NeumannBC(geom, lambda x: 0, boundary_r)
Hi @praksharma , Thank you for the suggestion.
I tried and I get the following error. Could you please have a look?
lambda x, on: np.array([on_boundary(x[i], on[i]) for i in range(len(x))])
To silence this warning, decorate the function with @tf.autograph.experimental.do_not_convert
Traceback (most recent call last):
File "I:\xxx\xxx\xxx_diff1d.py", line 79, in <module>
losshistory, train_state = model.train(iterations=10)
I am referring to the example provided here https://github.com/lululxvi/deepxde/blob/b3921720188f0bf9183c3997dc60e5b26c17ae48/docs/demos/pinn_forward/eulerbeam.rst
Hi @praksharma ,
When you have a chance to look into this, could you please let me know?
Sorry what was the error? Can you please paste the full error trace? It looks like you are using tensorflow.
Hello @praksharma ,
Thank you for your reply. Yes, I am using tensorflow.
Below is the complete code:
"""
Solving 1D concentration diffusion problem
References:
Boundary condition: https://github.com/lululxvi/deepxde/blob/b3921720188f0bf9183c3997dc60e5b26c17ae48/docs/demos/pinn_forward/eulerbeam.rst
Initial condition: https://github.com/lululxvi/deepxde/blob/b3921720188f0bf9183c3997dc60e5b26c17ae48/docs/demos/pinn_forward/ode.2nd.rst#L11
"""
import deepxde as dde
import numpy as np
def pde(x, y):
"""
:param x: 2-dimensional vector; x[:, 0:1] = x-coordinate; x[:, 1:] = t-coordinate
:param y: network output; i.e., solution y(x,t)
:return:
"""
dc_t = dde.grad.jacobian(y, x, i=0, j=1)
dc_xx = dde.grad.hessian(y, x, i=0, j=0)
d = 1
return (
dc_t
- d * dc_xx
)
def boundary_l(x, on_boundary):
"""
Because of rounding-off errors, dde.utils.isclose(x[0], 0)
:param x:
:param on_boundary: all boundary points
:return:
"""
return on_boundary and dde.utils.isclose(x[0], 0) # définit le boundary x=0, left
def boundary_r(x, on_boundary):
"""
Because of rounding-off errors, dde.utils.isclose(x[0], 0)
:param x:
:param on_boundary: all boundary points
:return:
"""
return on_boundary and dde.utils.isclose(x[0], 1) # définit le boundary x=L, right
if __name__ == '__main__':
geom = dde.geometry.Interval(0, 1)
timedomain = dde.geometry.TimeDomain(0, 1)
geomtime = dde.geometry.GeometryXTime(geom, timedomain)
# bc_l = dde.icbc.DirichletBC(geom, lambda x: 5, lambda _, on_boundary: boundary_l)
# bc_r = dde.icbc.NeumannBC(geom, lambda x: 0, lambda _, on_boundary: boundary_r)
bc_l = dde.icbc.DirichletBC(geomtime, lambda x: 5, boundary_l)
bc_r = dde.icbc.NeumannBC(geom, lambda x: 0, boundary_r)
ic = dde.icbc.IC(geomtime, lambda x: 1, lambda _, on_initial: on_initial)
data = dde.data.TimePDE(
geomtime,
pde,
[bc_l, bc_r, ic],
num_domain=40, # no. of training residual points sampled inside the domain
num_boundary=20, # no. of training points sampled on the boundary
num_initial=10, # initial residual points for initial conditions
# solution=func, # reference solution to compute error of the dde solution, can be ignored if no exact soln
num_test=10000, # points for testing the residual
)
layer_size = [2] + [32] * 3 + [1] # width 32, depth 3
activation = "tanh"
initializer = "Glorot uniform"
net = dde.nn.FNN(layer_size, activation, initializer)
model = dde.Model(data, net)
model.compile("adam", lr=0.001, metrics=["l2 relative error"])
losshistory, train_state = model.train(iterations=10)
dde.saveplot(losshistory, train_state, issave=True, isplot=True)
Could you please try running?
Error:
WARNING:tensorflow:AutoGraph could not transform <function
coding=utf-8
lambda x, on: np.array([on_boundary(x[i], on[i]) for i in range(len(x))])
To silence this warning, decorate the function with @tf.autograph.experimental.do_not_convert
WARNING:tensorflow:AutoGraph could not transform <function
coding=utf-8
lambda x, on: np.array([on_boundary(x[i], on[i]) for i in range(len(x))])
To silence this warning, decorate the function with @tf.autograph.experimental.do_not_convert
Traceback (most recent call last):
File "I:\c2s\simgraph\simdeep_diff1d.py", line 80, in