Documentation for residual-based adaptive sampling

[SamanHooshyar]

Hi,

Thank you for constructing and publishing the DeepXDE package. I was wondering if you could tell me where I can find documentation on implementing residual-based adaptive sampling and gradient-enhanced PINN. I am trying different methods of sampling collocation points to improve my network accuracy.

Thanks,

[lululxvi]

• https://arxiv.org/abs/2207.10289
• https://doi.org/10.1016/j.cma.2022.114823

[SamanHooshyar]

Thank you for your reply. Is there a library in DeepXDE package that could be used to implement adaptive sampling, or should I implement it myself by following the given algorithms in the above articles?

[lululxvi]

Implement it yourself. See the github links in the papers.

[elliot-hicks]

@SamanHooshyar DeepXDE has an example of doing RAR in their examples, it follows this structure:

n_new = 1000 # number of new samples
x, y = np.linspace(0, 1, 101), np.linspace(0, 1, 101)
x, y = np.meshgrid(x, y) # test distribution
X = np.stack([x.flatten(), y.flatten()], axis=-1)

for i in range(5):
    f = np.array(model.predict(X, operator=<your pde system>)) # get residuals from PDE system
    e = np.square(f) 
    e =  np.sum(e, axis = 0) # aggregate across the multiple losses for each point using SE
    x_id = np.argsort(e, axis = 0)[:n_new] # sort and select n_new worst performing points
    new_points = np.squeeze(X[x_id])
    print("Adding ",len(x_id)," new points. \n") 
    solver.add_anchors(new_points) # add them as anchors
    solver.resample_train_points() # optional
    model.compile("adam", lr = 1e-4)
    loss_history, train_state = model.train(iterations=10000, display_every = 10000) # train again
    
    # repeat until certain condition met or for a certain amount of resamples (5 here)
    
dde.saveplot(loss_history, train_state, issave=False, isplot=True)

[SamanHooshyar]

@elliot-hicks Thank you this was helpful!