动量法应用NASA测试不同飞机机翼噪音

%matplotlib inline
from mxnet import nd
import numpy as np
from mxnet import autograd,gluon,init,nd
from mxnet.gluon import nn,data as gdata,loss as gloss
import time

def get_data():
    data = np.genfromtxt('./data/airfoil_self_noise.dat', delimiter='\t')
    data = (data - data.mean(axis=0)) / data.std(axis=0)
    return nd.array(data[:1500, :-1]), nd.array(data[:1500, -1])

features, labels = get_data()
features[0]
labels[0]

# 定义网络
def linreg(X,w,b):
    return nd.dot(X,w) + b

# 平方损失
def squared_loss(y_hat,y):
    return (y_hat - y.reshape(y_hat.shape))**2/2

# 初始化参数
def init_momentum_states():
    v_w = nd.zeros((features.shape[1], 1))
    v_b = nd.zeros(1)
    return (v_w, v_b)

# params [w,b]
# states [v_w,v_b] 初始化状态
# hyperparams {'lr':0.02,'momentum':0.5}
def sgd_momentum(params, states, hyperparams):
    for p, v in zip(params, states):
        v[:] = hyperparams['momentum'] * v + hyperparams['lr'] * p.grad
        p[:] -= v

def train(trainer_fn, states, hyperparams, features, labels,
              batch_size=10, num_epochs=2):
    # 初始化模型。
    net, loss = gb.linreg, gb.squared_loss
    w = nd.random.normal(scale=0.01, shape=(features.shape[1], 1))
    b = nd.zeros(1)
    w.attach_grad()
    b.attach_grad()

    def eval_loss():
        return loss(net(features, w, b), labels).mean().asscalar()

    ls = [eval_loss()]
    data_iter = gdata.DataLoader(
        gdata.ArrayDataset(features, labels), batch_size, shuffle=True)
    for _ in range(num_epochs):
        start = time.time()
        for batch_i, (X, y) in enumerate(data_iter):
            with autograd.record():
                l = loss(net(X, w, b), y).mean()  # 使用平均损失。
            l.backward()
            trainer_fn([w, b], states, hyperparams)  # 迭代模型参数。
            if (batch_i + 1) * batch_size % 100 == 0:
                ls.append(eval_loss())  # 每 100 个样本记录下当前训练误差。
    # 打印结果和作图。
    print('loss: %f, %f sec per epoch' % (ls[-1], time.time() - start))
    gb.set_figsize()
    gb.plt.plot(np.linspace(0, num_epochs, len(ls)), ls)
    gb.plt.xlabel('epoch')
    gb.plt.ylabel('loss')

train(trainer_fn=sgd_momentum,states= init_momentum_states(),hyperparams={'lr': 0.02, 'momentum': 0.5}, features=features, labels=labels)

train(sgd_momentum,init_momentum_states(),{'lr':0.02,'momentum':0.9},features,labels)

train(sgd_momentum,init_momentum_states(),{'lr':0.004,'momentum':0.9},features,labels)

gluon 版：

def train_gluon(trainer_name,trainer_hyperparams,features,labels,batch_size=10,num_epochs=2):
    # 初始化模型
    net = nn.Sequential()
    net.add(nn.Dense(1))
    net.initialize(init.Normal(sigma=0.01))
    loss = gloss.L2Loss()

    def eval_loss():
        return loss(net(features),labels).mean().asscalar()

    ls = [eval_loss()]
    data_iter = gdata.DataLoader(gdata.ArrayDataset(features,labels),batch_size,shuffle=True)

    # 创建 Trainer 实例迭代模型参数
    trainer = gluon.Trainer(net.collect_params(),trainer_name,trainer_hyperparams)

    for _ in range(num_epochs):
        start = time.time()
        for batch_i, (X,y) in enumerate(data_iter):
            with autograd.record():
                l = loss(net(X),y)
            l.backward()
            trainer.step(batch_size)
            if (batch_i + 1) * batch_size % 100 ==0:
                ls.append(eval_loss())

    # 打印结果和作图。
    print('loss: %f, %f sec per epoch' % (ls[-1], time.time() - start))
    gb.set_figsize()
    gb.plt.plot(np.linspace(0, num_epochs, len(ls)), ls)
    gb.plt.xlabel('epoch')
    gb.plt.ylabel('loss')

train_gluon('sgd',{'learning_rate':0.004,'momentum':0.9},features,labels)