DeepXDE在paddle backend下使用L-BFGS优化器出现错误结果

[HongtaoBi]

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运行DeepXDE的一个官方案例时，使用pytorch的backend运行adam优化器和L-BFGS优化器能够得到想要的结果，但转换为paddle backend后训练时得到错误的结果。

代码为：https://github.com/lululxvi/deepxde/blob/master/docs/demos/pinn_forward/allen.cahn.rst

"""Backend supported: tensorflow.compat.v1, tensorflow, pytorch, paddle

Implementation of Allen-Cahn equation example in paper https://arxiv.org/abs/2111.02801.
"""
import deepxde as dde
import numpy as np
from scipy.io import loadmat
# Import tf if using backend tensorflow.compat.v1 or tensorflow
# from deepxde.backend import tf
# Import torch if using backend pytorch
# import torch
# Import paddle if using backend paddle
import paddle

def gen_testdata():
    data = loadmat("../dataset/Allen_Cahn.mat")

    t = data["t"]
    x = data["x"]
    u = data["u"]

    dt = dx = 0.01
    xx, tt = np.meshgrid(x, t)
    X = np.vstack((np.ravel(xx), np.ravel(tt))).T
    y = u.flatten()[:, None]
    return X, y

geom = dde.geometry.Interval(-1, 1)
timedomain = dde.geometry.TimeDomain(0, 1)
geomtime = dde.geometry.GeometryXTime(geom, timedomain)
d = 0.001

def pde(x, y):
    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 - d * dy_xx - 5 * (y - y**3)

# Hard restraints on initial + boundary conditions
# # Backend tensorflow.compat.v1 or tensorflow
# def output_transform(x, y):
#     return x[:, 0:1]**2 * tf.cos(np.pi * x[:, 0:1]) + x[:, 1:2] * (1 - x[:, 0:1]**2) * y

# # Backend pytorch
# def output_transform(x, y):
#     return x[:, 0:1]**2 * torch.cos(np.pi * x[:, 0:1]) + x[:, 1:2] * (1 - x[:, 0:1]**2) * y

# Backend paddle
def output_transform(x, y):
    return x[:, 0:1]**2 * paddle.cos(np.pi * x[:, 0:1]) + x[:, 1:2] * (1 - x[:, 0:1]**2) * y

data = dde.data.TimePDE(geomtime, pde, [], num_domain=8000, num_boundary=400, num_initial=800)
net = dde.nn.FNN([2] + [20] * 3 + [1], "tanh", "Glorot normal")
net.apply_output_transform(output_transform)
model = dde.Model(data, net)

model.compile("adam", lr=1e-3)
model.train(iterations=40000)
model.compile("L-BFGS")
losshistory, train_state = model.train()
dde.saveplot(losshistory, train_state, issave=True, isplot=True)

X, y_true = gen_testdata()
y_pred = model.predict(X)
f = model.predict(X, operator=pde)
print("Mean residual:", np.mean(np.absolute(f)))
print("L2 relative error:", dde.metrics.l2_relative_error(y_true, y_pred))
np.savetxt("test.dat", np.hstack((X, y_true, y_pred)))

使用pytorch backend在L-BFGS优化器开始时的loss为：

使用paddle backend在L-BFGS优化器开始时的loss为：

如果能提供帮助的话十分感谢！

[lijialin03]

感谢您的反馈，可以拉一下DeepXDE最新代码，应该已经改了