gPINN and RAS in DeepXDE

[ryabs07]

Hi all,
Is there already a framework for gradient-enhanced physics-informed neural network (gPINN) and residual-based adaptive sampling (RAS) in DeepXDE?

I read the paper related to these topics that are mentioned in the introduction markdown of DeepXDE and was wondering how we can implement them within DeepXDE.
Thanks in advance :)

[xuelanghanbao]

I hope this Poisson equation in 1D example can help you understand how to implement gPINN and RAS(RAR is one of the RAS methods) based on DeepXDE

import numpy as np
import deepxde as dde
import deepxde.backend as bkd
import matplotlib.pyplot as plt

def pde(x, y):
    # PINN
    # dy_xx = dde.grad.hessian(y, x)
    # res = -dy_xx - np.pi ** 2 * bkd.sin(np.pi * x)
    # return res

    # gPINN
    dy_xx = dde.grad.hessian(y, x)
    res = -dy_xx - np.pi**2 * bkd.sin(np.pi * x)
    g_res = dde.grad.jacobian(res, x)
    return [res, g_res]

def boundary(x, on_boundary):
    return on_boundary

def func(x):
    return np.sin(np.pi * x)

geom = dde.geometry.Interval(-1, 1)
bc = dde.icbc.DirichletBC(geom, func, boundary)
data = dde.data.PDE(geom, pde, bc, 16, 2, solution=func, num_test=100)

layer_size = [1] + [50] * 3 + [1]
activation = "tanh"
initializer = "Glorot uniform"
net = dde.nn.FNN(layer_size, activation, initializer)

model = dde.Model(data, net)

# PINN
# model.compile("adam", lr=0.001, metrics=["l2 relative error"])
# losshistory, train_state = model.train(iterations=10000)
# dde.saveplot(losshistory, train_state, issave=True, isplot=True)

# RAR
model.compile("adam", lr=1.0e-3)
model.train(iterations=10000)
model.compile("L-BFGS")
model.train()

X = geom.random_points(100000)
err = 1
while err > 0.005:
    f = model.predict(X, operator=pde)
    err_eq = np.absolute(f)
    err = np.mean(err_eq)
    print("Mean residual: %.3e" % (err))

    x_id = np.argmax(err_eq)
    print("Adding new point:", X[x_id], "\n")
    data.add_anchors(X[x_id])
    early_stopping = dde.callbacks.EarlyStopping(min_delta=1e-4, patience=2000)
    model.compile("adam", lr=1e-3)
    model.train(epochs=10000, disregard_previous_best=True, callbacks=[early_stopping])
    model.compile("L-BFGS")
    losshistory, train_state = model.train()

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

[ryabs07]

Thank you for the suggestions.
For my problem statements, random sampling in geomtime domain was performing quite badly. I started to get good results after switching to gridded sampling method using anchoring. I guess, if i am already using anchored points with fine resolution gridded sampling, using the RAR method would not have significant impact on my problem.
Nevertheless, thank you very much for your kind suggestions. :)