Neumann boundary conditions error distribution

[marijanarra]

Hi Lu,

Thank you once again for this great library.

I couldn't find a good way to retrieve the BC value error distribution for Neumann BC on the boundaries. Do you maybe have an advice on how to do this?

Thanks!

[lululxvi]

I don't have a good answer now. You can simply predict the values of functions and its gradients, and then compute the error by yourself.

[marijanarra]

  def first_derivative(x, y):
      return tf.stack([dde.grad.jacobian(y, x, j=0), dde.grad.jacobian(y, x, j=1) ], axis=1)[:,:,0]

    domain_pts = geom.random_points(test_points_num)
    prediction_error_domain = abs(model.predict(domain_pts, operator=pde))
    first_derivative_test = model.predict(data.test_x, operator=first_derivative)
    bcs_start = np.cumsum([0] + data.num_bcs)
    
    bcs_pts = []
    bc_errors = []
    for j, bc in enumerate(bcs):
        beg, end = bcs_start[j], bcs_start[j + 1]
        pts = data.test_x[beg:end]
        bcs_pts.extend(pts)
        bc_val = bc.func(pts, 0, len(pts), None).numpy()
        bc_val_predict = np.sum(first_derivative_test[beg:end] * normal_sign * geom.boundary_normal(pts), axis=1, keepdims=1)
        bc_errors.extend(abs(bc_val-bc_val_predict))
    
    geom_pts =  np.vstack((domain_pts,  np.array(bcs_pts)))
    geom_errors = np.vstack((prediction_error_domain, np.array(bc_errors)))
    
    fig = plt.figure()
    ax = plt.axes()
    sctr = ax.scatter(geom_pts[:,0], geom_pts[:,1], s=1.0, c=geom_errors)
    fig.colorbar(sctr, ax=ax)
    plt.title("Test points prediction error")
    plt.savefig(dir_path + 'bc_error.png')
    plt.show()

In case someone will need it, this was my solution. This plots the PDE error inside the domain and Neumann BCs errors on the boundaries.