OperatorBC does not match DirichletBC

[voloddia]

Hi Lu, Thanks for the great library. I am learning how to use OperatorBC. As a sanity check, I did an experiment to see if OperatorBC can match DirichletBC. The code is exactly the same as in diffusion_1D.py except that I define a function bc to return 0 and feed it into OperatorBC.

def bc(x, y, X): 
    return np.zeros((len(X), 1))

geom = dde.geometry.Interval(-1, 1)
timedomain = dde.geometry.TimeDomain(0, 1)
geomtime = dde.geometry.GeometryXTime(geom, timedomain)

# changed bc
bc = dde.OperatorBC(geomtime, bc, lambda _, on_boundary: on_boundary)
ic = dde.IC(geomtime, func, lambda _, on_initial: on_initial)
data = dde.data.TimePDE(
    geomtime,
    pde,
    [bc, ic],
    num_domain=40,
    num_boundary=20,
    num_initial=10,
    solution=func,
    num_test=10000,
)

The results are quite different. Did I define bc incorrectly?

• DirichletBC
• OperatorBC // Train loss for BC is 0 although it looks like BC is not satisfied?

  Step      Train loss                        Test loss                         Test metric   
  0         [1.59e+01, 0.00e+00, 7.99e-01]    [1.70e+01, 0.00e+00, 0.00e+00]    [1.26e+00]    
  1000      [1.96e-03, 0.00e+00, 4.71e-04]    [8.02e-03, 0.00e+00, 0.00e+00]    [3.03e-01]    
  2000      [7.86e-04, 0.00e+00, 5.22e-05]    [2.32e-03, 0.00e+00, 0.00e+00]    [4.31e-01]    
  3000      [3.92e-03, 0.00e+00, 5.67e-05]    [3.87e-03, 0.00e+00, 0.00e+00]    [4.81e-01]    
  4000      [1.08e-03, 0.00e+00, 1.20e-05]    [1.50e-03, 0.00e+00, 0.00e+00]    [5.06e-01]    
  5000      [5.13e-04, 0.00e+00, 4.94e-06]    [1.05e-03, 0.00e+00, 0.00e+00]    [5.17e-01]    
  6000      [4.67e-05, 0.00e+00, 2.01e-06]    [5.34e-04, 0.00e+00, 0.00e+00]    [5.22e-01]    
  7000      [8.53e-05, 0.00e+00, 2.58e-06]    [5.62e-04, 0.00e+00, 0.00e+00]    [5.27e-01]    
  8000      [2.59e-05, 0.00e+00, 2.05e-06]    [4.66e-04, 0.00e+00, 0.00e+00]    [5.29e-01]    
  9000      [6.46e-04, 0.00e+00, 9.27e-06]    [7.91e-04, 0.00e+00, 0.00e+00]    [5.30e-01]    
  10000     [1.12e-04, 0.00e+00, 2.53e-06]    [4.90e-04, 0.00e+00, 0.00e+00]    [5.33e-01]    

[lululxvi]

The OperatorBC should return the error, i.e.,

def bc(x, y, X): 
    return y - 0

[voloddia]

I got it. Thank you very much, Dr. Lu.