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In the following codes, it should be |
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Thank you so much for your reply. After adding the tf.abs(), the code can be run. but I find the loss is still very large after training 10,000 epochs. the loss didn't change a lot during training except the first column. Do you have any ideas to deal with it?
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For unbalanced losses, try some coefficients. Also use Adam optmiser when these second order optimisers don’t work. |
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After seeing FAQ, I did some solutions like Use loss_weights for rescaling, Train with more iterations. I tried to use dde.config.set_default_float('float64'), but it showed en error. ##############parameters####################
C_s = 890 #[j/(kg*K)]
C_w = 4200 #[j/(kg*K)]
C_i = 2100 #[j/(kg*K)]
lamda_s = 1.38 #[W/(m*K)]
lamda_w = 0.63 #[W/(m*K)]
lamda_i = 2.31 #[W/(m*K)]
L = 334560 #[J/kg]
rho_i = 918 #[kg/m^3]
rho_w = 1000 #[kg/m^3]
rho_s = 1700 #[kg/m^3]
theta_s=0.25
theta_r = 0.08
T_f = 272.97 #[K]
B=0.55
k_s=1e-5 #[m/s]
l=0.5
m=0.5
a=2
S0=0.6
@tf.function
def k_r(S):
return tf.where(tf.math.less(S,1),tf.abs(S)**l*(1-tf.abs(1-tf.abs(S)**(1/m))**m)**2, 1)
@tf.function
def k(S):
k = k_s*k_r(S)
return k
@tf.function
def c(S):
return tf.where(tf.math.less(S,1),a*m/(1-m)*(theta_s-theta_r)*tf.abs(S)**(1/m)*tf.abs(1-tf.abs(S)**(1/m))**m,0.001)
@tf.function
def theta_w(S):
# theta_w = tf.where(tf.math.less(S,1) & tf.math.greater(S,0), (theta_s-theta_r)*S+theta_r,
# tf.where(tf.math.less_equal(S,0), theta_r, theta_s))
theta_w = tf.where(tf.math.less(S,1),tf.where(tf.math.less_equal(S,0),theta_r,(theta_s-theta_r)*S+theta_r),theta_s)
return theta_w
@tf.function
def Bi(T):
return tf.where(tf.math.less(T, T_f) , 1.1*tf.abs(T/T_f)**B-1.1, 0)
@tf.function
def theta_i(T,S):
return Bi(T)*theta_w(S)
@tf.function
def lz(T,S):
return 10**(-10*theta_i(T,S))
@tf.function
def D(T,S):
return k(S)/(c(S)*lz(T,S))
@tf.function
def lamda(T,S):
return theta_w(S)*lamda_w+theta_i(T,S)*lamda_i+(1-theta_s)*lamda_s
@tf.function
def rho_C(T,S):
return theta_w(S)*rho_w*C_w+theta_i(T,S)*rho_i*C_i+(1-theta_s)*rho_s*C_s
def PDE(x,y):
X, Y ,t=x[:,0:1],x[:,1:2], x[:,2:3]
T,S = y[:,0:1],y[:,1:2]
#########equations##########################
dT_t = dde.grad.jacobian(y, x, i=0, j=2)
dT_xx = dde.grad.hessian(y, x, component=0, i=0,j=0)
dT_yy = dde.grad.hessian(y, x, component=0, i=1,j=1)
dS_xx = dde.grad.hessian(y, x, component=1, i=0,j=0)
dS_yy = dde.grad.hessian(y, x, component=1, i=1,j=1)
dS_t = dde.grad.jacobian(y, x, i=1, j=2)
dBi_T = tf.where(tf.math.less(T,T_f),1.1*B*tf.abs(T/T_f)**(B-1)*1/T_f,0)
dBi_t = dBi_T*dT_t
#### temperature field ####
da_T = rho_C(T,S)-L*rho_i*((theta_s-theta_r)*S+theta_r)*dBi_T
c_T = lamda(T,S)
f_T = L*rho_i*(theta_s-theta_r)*Bi(T)*dS_t
eq1 = da_T*dT_t-c_T*(dT_xx+dT_yy)-f_T
#### water field ####
c_W = D(T,S)
a_W = rho_i/rho_w*dBi_t
f_W = -rho_i/rho_w*(theta_r/(theta_s-theta_r))*dBi_t
da_w = 1+rho_i/rho_w*Bi(T)
eq2 = da_w*dS_t - c_W*(dS_xx+dS_yy)+a_W*S - f_W
return [eq1,eq2]
geom = dde.geometry.Rectangle([0, 0], [0.1, 0.2])
timedomain = dde.geometry.TimeDomain(0, 72)
geomtime = dde.geometry.GeometryXTime(geom, timedomain)
### boundary condition ####
def left_boundary(x, on_boundary):
return on_boundary and np.isclose(x[0], 0)
def right_boundary(x, on_boundary):
return on_boundary and np.isclose(x[0], 0.1)
def bottom_boundary(x,on_boundary):
return on_boundary and np.isclose(x[1], 0)
def upper_boundary(x,on_boundary):
return on_boundary and np.isclose(x[1], 0.2)
def zero_(x):
return 0
def two_(x):
return 275.15
def Tu(x):
return 263.15
# return tf.where(tf.math.greater(x,0) & tf.math.less(x,1),2,
# tf.where(tf.math.greater(x,60) & tf.math.less(x,72),2,
# tf.where(tf.math.greater(x,24) & tf.math.less(x,36),-10,
# tf.where(tf.math.greater(x,1) & tf.math.less(x,24),-12/23*x+58/23, 7/6*x-344/7))))
bcT1 = dde.NeumannBC(geomtime,zero_,left_boundary,component=0)
bcT2 = dde.NeumannBC(geomtime,zero_,right_boundary,component=0)
bcT3 = dde.icbc.DirichletBC(geomtime,two_,bottom_boundary,component=0)
bcT4 = dde.icbc.DirichletBC(geomtime,Tu,upper_boundary,component=0)
bcS1 = dde.NeumannBC(geomtime,zero_,left_boundary,component=1)
bcS2 = dde.NeumannBC(geomtime,zero_,right_boundary,component=1)
bcS3 = dde.NeumannBC(geomtime,zero_,bottom_boundary,component=1)
bcS4 = dde.NeumannBC(geomtime,zero_,upper_boundary,component=1)
icT1 = dde.icbc.IC(geomtime, lambda x: 275.15, lambda _, on_initial: on_initial, component=0)
icS1 = dde.icbc.IC(geomtime, lambda x: S0, lambda _, on_initial: on_initial, component=1)
#bcT1,bcT2,bcT3,bcT4,bcS1,bcS2,bcS3,bcS4,icT1,icS1
data = dde.data.TimePDE(
geomtime, PDE, [bcT1,bcT2,bcT3,bcT4,bcS1,bcS2,bcS3,bcS4,icT1,icS1], num_domain=10000, num_boundary=3000, num_initial=2000,num_test=20000
)
net = dde.nn.FNN([3] + [50] * 3 + [2], "tanh", "Glorot normal")
# net.outputs_modify(lambda x, y: y * 100)
model = dde.Model(data, net)
model.compile("adam", lr=0.001)
losshistory, train_state = model.train(0)
initial_losses =losshistory.loss_train[0]
loss_weights = 1 / initial_losses
model.compile("adam", lr=1e-5,loss_weights=loss_weights)
# pde_residual_resampler = dde.callbacks.PDEResidualResampler(period=1)
model.train(epochs=50000)
model.compile("L-BFGS")
losshistory, train_state = model.train()
dde.saveplot(losshistory, train_state, issave=True, isplot=True)but the results continues to have nan after several training. The T, S range in this code should be T>0 and 0=<S<=1. What could I do to make sure the program know this? |
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This is my code to solve a coupled temperature (T) and saturate (S) problem.
I got an nan when the epochs is 1000. and got an warning:
Rectangle boundary_normal called on vertices. You may use PDE(..., exclusions=...) to exclude the vertices.
Does anyone know how to deal with it?
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