I want to Solve Lorenz System

[Msnaldin-64]

Dear Dr. Lu Lu
I have just started to use Deepxde this week and I'm very interested in. I'm trying to solve Lorenz System with the following code but the results are far from being in the right shape. Could you kindly assist me in correcting the code. Thank you in advance.

import deepxde as dde
import matplotlib.pyplot as plt
import numpy as np
from scipy import integrate
from deepxde.backend import tf

def Lorenz_system(x, y):
"""Lorenz system.
dy1/dx = 10 * (y2 - y1)
dy2/dx = y1 * (28 - y3) - y2
dy3/dx = y1 * y2 - 8/3 * y3
"""
y1, y2, y3 = y[:, 0:1], y[:, 1:2], y[:, 2:]
dy1_x = dde.grad.jacobian(y1, x, i=0)
dy2_x = dde.grad.jacobian(y2, x, i=0)
dy3_x = dde.grad.jacobian(y3, x, i=0)
return [
dy1_x - 10.0 * (y2 - y1),
dy2_x - y1 * (28 - y3) + y2,
dy3_x - y1 * y2 + 8.0/3.0 * y3,
]

def boundary(_, on_initial):
return on_initial

geom = dde.geometry.TimeDomain(0, 50)
ic1 = dde.icbc.IC(geom, lambda x: 1.0, boundary, component=0)
ic2 = dde.icbc.IC(geom, lambda x: 1.0, boundary, component=1)
ic3 = dde.icbc.IC(geom, lambda x: 1.0, boundary, component=2)
data = dde.data.PDE(geom, Lorenz_system, [ic1, ic2, ic3], 3500, 2, solution=None, num_test=100)

layer_size = [1] + [64] * 6 + [3]
activation = "tanh"
initializer = "Glorot uniform"
net = dde.nn.FNN(layer_size, activation, initializer)

def input_transform(t):
return tf.concat(
(
t,
tf.sin(t),
tf.sin(2 * t),
tf.sin(3 * t),
tf.sin(4 * t),
tf.sin(5 * t),
tf.sin(6 * t),
),
axis=1,
)

def output_transform(t, y):
y1 = y[:, 0:1]
y2 = y[:, 1:2]
y3 = y[:, 2:3]
return tf.concat([y1 * tf.tanh(t) + 1, y2 * tf.tanh(t) + 1, y3 * tf.tanh(t) + 1], axis=1)

net.apply_feature_transform(input_transform)
net.apply_output_transform(output_transform)
model = dde.Model(data, net)

model.compile("adam", lr=0.001)
losshistory, train_state = model.train(iterations=50000)

Most backends except jax can have a second fine tuning of the solution

model.compile("L-BFGS")
losshistory, train_state = model.train()
dde.saveplot(losshistory, train_state, issave=True, isplot=True)