Inverse Burger's Equation not working

[nirmal129]

Hello,

I am trying to solve the inverse Burger's Equation to find $\eta_{nn}$ in $y_t + y * y_x - \eta_{nn} * 10^{-3} * y_{xx} = 0$. The true value of $\eta$ is 3.183. However, the PINN is not approaching the correct value. The value starts from 1 and just keeps increasing with the training.

Could someone suggest me any improvements or help me debug my code so I can get the true $\eta$ value?

The code:

geom = dde.geometry.Interval(x_min, x_max)
timedomain = dde.geometry.TimeDomain(t_min, t_max)
geomtime = dde.geometry.GeometryXTime(geom, timedomain)

eta_nn = dde.Variable(1.0)

def pde(x, y):
    dy_x = dde.grad.jacobian(y, x, i=0, j=0)
    dy_t = dde.grad.jacobian(y, x, i=0, j=1)
    dy_xx = dde.grad.hessian(y, x, i=0, j=0)
    return dy_t + y * dy_x - eta_nn * 1e-3 * dy_xx

# Boundary
bc = dde.icbc.DirichletBC(
    geomtime,
    lambda x: 0,
    lambda _, on_boundary: on_boundary
)

# Initial condition
ic = dde.icbc.IC(
    geomtime,
    lambda x: -tf.sin(np.pi * x[:, 0:1]),
    lambda _, on_initial: on_initial
)

# Data
observe_y = dde.icbc.PointSetBC(XT, y_data, component=0)

data = dde.data.TimePDE(
    geomtime,
    pde,
    [bc, ic, observe_y],
    num_domain=N_r,
    num_boundary=N_b,
    num_initial=N_i,
    anchors=XT,
    num_test=5000,
)

net = dde.nn.FNN([2, 20, 20, 20, 1], "tanh", "Glorot uniform")

model = dde.Model(data, net)
pde_residual_resampler = dde.callbacks.PDEPointResampler()
variable = dde.callbacks.VariableValue([eta_nn], period=1000, filename="variables.dat")
loss_weights = [1., 1., 1.]

model.compile("adam", lr=0.001, external_trainable_variables=[eta_nn])
losshistory, train_state = model.train(iterations=num_iter, callbacks=[pde_residual_resampler, variable])

model.compile("L-BFGS", external_trainable_variables=[eta_nn])
losshistory, train_state = model.train(callbacks=[pde_residual_resampler, variable])

dde.saveplot(losshistory, train_state, issave=True, isplot=True)

The result: