Periodic IC

[ehsanngh]

Hello,

I'm trying to solve a system of PDEs with two variables in space domain and one time variable. One of my condition is that the value at the end of time interval is equal to its initial value. Is it possible to implement this initial condition?

Thanks.

[forxltk]

Use PeriodicBC. You can use z as time variable.

[ehsanngh]

Thanks for your answer. Could you show me how to do that?

[forxltk]

https://deepxde.readthedocs.io/en/latest/demos/pinn_forward/poisson.1d.dirichletperiodic.html

[athtareq]

Hello, this is an example I did for $ u_t $ + $ \nabla u $ = $ f $ and $ u(0)=u(1) $

It's also two space variables and one time variable, and the solution is time-periodic

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

import numpy as np
import tensorflow as tf

import deepxde as dde

import tensorflow_addons as tfa

from tensorflow_addons import activations


from matplotlib import pyplot


def func(x,y,t):
    return 2*np.pi*(x+y)*tf.cos(2.0*np.pi*t)
def pde (x , y) :
    grad_y = tf . gradients (y , x ) [0]
    dy_x , dy_y , dy_t = grad_y [: , 0:1] , grad_y [: , 1:2],grad_y [: , 2:]
    dy_xx = tf . gradients ( dy_x , x ) [0][: , 0:1]
    dy_yy = tf . gradients ( dy_y , x ) [0][: , 1:2]
    return dy_t - (dy_xx + dy_yy) - func(x[: , 0:1],x[: , 1:2],x[: , 2:])

def func_bdy(x):
    return np.zeros([len(x),1])

def boundary_time(x, on_boundary):
    return on_boundary and (np.isclose(x[2], 0) or np.isclose(x[2], 1))    


domain = dde.geometry.Cuboid(xmin=[0, 0, 0], xmax=[1, 1, 1])

def space_boundary(x, on_boundary):
    return on_boundary and (np.isclose(x[0]**2-1, 0) or np.isclose(x[1]**2-1, 0))

def time_boundary(x, domain):
    return domain and (np.isclose(x[2], 0) or np.isclose(x[2], 1))

def boundary_b(x, on_boundary):
    return on_boundary and np.isclose(x[1], 0)

def boundary_t(x, on_boundary):
    return on_boundary and np.isclose(x[1], 1)

def boundary_r(x, on_boundary):
    return on_boundary and np.isclose(x[0], 1)

def boundary_l(x, on_boundary):
    return on_boundary and np.isclose(x[0], 0)

pbc1 = dde.PeriodicBC(domain, 2, time_boundary, component=0)
bc1 = dde.DirichletBC(domain, func_bdy, boundary_b, component=0)
bc2 = dde.DirichletBC(domain, func_bdy, boundary_t, component=0)
bc3 = dde.DirichletBC(domain, func_bdy, boundary_r, component=0)
bc4 = dde.DirichletBC(domain, func_bdy, boundary_l, component=0)


data = dde.data.TimePDE(
    domain, pde, [bc1,bc2,bc3,bc4,pbc1], num_domain=1000, num_boundary=1000, num_test=10000
)
metrics_=None
net = dde.maps.FNN([3] + [50] * 3 + [1], "tanh", "Glorot uniform")
model2 = dde.Model(data, net)

model2.compile("adam", lr=0.001, metrics=metrics_,loss='MSE')
model2.train(epochs=30000)
model2.compile("L-BFGS-B", metrics=metrics_)
losshistory, train_state = model2.train(model_save_path='parabolic')
dde.saveplot(losshistory, train_state, issave=True, isplot=True)


 

[ehsanngh]

Thank you so much! It helped me solve my problem.