pointwise 例子

Pointwise是一个将有限元数据进行离散化和插值的软件程序。它被广泛应用于CAD建模、流体动力学、有限元分析和声学等领域。以下是一个关于Pointwise的例子：

在航空航天工程中，Pointwise可以被用来生成飞机的外形轮廓。首先，航空工程师会根据飞机的设计需求和性能要求利用CAD软件绘制飞机的三维模型。然后，将该模型导入到Pointwise中进行处理。

在Pointwise中，航空工程师可以定义不同的几何参数，例如翼展、燃油箱位置和机翼弯曲等，并将这些参数应用到飞机的外形轮廓上。通过调整这些参数，航空工程师可以对飞机进行快速的设计迭代，以优化飞机的性能。

接下来，航空工程师会选择适当的网格生成方法。Pointwise提供了多种网格生成算法，例如结构化网格生成、非结构化网格生成和混合网格生成等。航空工程师可以根据飞机的复杂性和分析要求选择合适的算法。

最后，航空工程师可以在Pointwise中生成飞机的网格。该网格可以用于后续的流体动力学模拟，以评估飞机在不同飞行条件下的气动性能。

通过Pointwise，航空工程师可以高效地进行飞机的几何建模和网格生成。这样的过程不仅可以提高设计效率，还可以减少飞机设计中的错误和不确定性，从而更好地满足飞机设计的要求。

相关问题

有没有transformer的例子

是的，以下是一个使用Transformer模型进行文本分类的示例：

import tensorflow as tf
import tensorflow_datasets as tfds

# 加载IMDB数据集
(train_data, test_data), info = tfds.load('imdb_reviews/subwords8k', 
                                         split=(tfds.Split.TRAIN, tfds.Split.TEST), 
                                         with_info=True, as_supervised=True)
encoder = info.features['text'].encoder

BUFFER_SIZE = 10000
BATCH_SIZE = 64

# 训练数据和测试数据预处理
padded_shapes = ([None], ())
train_batches = (train_data.shuffle(BUFFER_SIZE).padded_batch(BATCH_SIZE, padded_shapes=padded_shapes))
test_batches = (test_data.padded_batch(BATCH_SIZE, padded_shapes=padded_shapes))

# Transformer模型定义
class TransformerModel(tf.keras.Model):
    def __init__(self, num_layers, d_model, num_heads, dff, input_vocab_size, target_vocab_size, dropout_rate=0.1):
        super(TransformerModel, self).__init__()

        self.encoder = tf.keras.layers.Embedding(input_vocab_size, d_model)
        self.pos_encoding = positional_encoding(input_vocab_size, d_model)

        self.transformer_blocks = [TransformerBlock(d_model, num_heads, dff, dropout_rate) for _ in range(num_layers)]
        self.dropout = tf.keras.layers.Dropout(dropout_rate)
        self.final_layer = tf.keras.layers.Dense(target_vocab_size)

    def call(self, inputs, training):
        input_seq, input_mask = inputs
        input_emb = self.encoder(input_seq)
        input_emb *= tf.math.sqrt(tf.cast(self.encoder.embedding_dim, tf.float32))
        input_emb += self.pos_encoding[:input_emb.shape[1], :]

        x = self.dropout(input_emb, training=training)

        for i in range(len(self.transformer_blocks)):
            x = self.transformer_blocks[i](x, input_mask, training)

        x = tf.reduce_mean(x, axis=1)
        x = self.final_layer(x)

        return x

# Transformer块定义
class TransformerBlock(tf.keras.layers.Layer):
    def __init__(self, d_model, num_heads, dff, dropout_rate=0.1):
        super(TransformerBlock, self).__init__()

        self.multi_head_attention = MultiHeadAttention(d_model, num_heads)
        self.feed_forward_network = point_wise_feed_forward_network(d_model, dff)

        self.layer_norm1 = tf.keras.layers.LayerNormalization(epsilon=1e-6)
        self.layer_norm2 = tf.keras.layers.LayerNormalization(epsilon=1e-6)

        self.dropout1 = tf.keras.layers.Dropout(dropout_rate)
        self.dropout2 = tf.keras.layers.Dropout(dropout_rate)

    def call(self, x, mask, training):
        attn_output, _ = self.multi_head_attention(x, x, x, mask)
        attn_output = self.dropout1(attn_output, training=training)
        out1 = self.layer_norm1(x + attn_output)

        ffn_output = self.feed_forward_network(out1)
        ffn_output = self.dropout2(ffn_output, training=training)
        out2 = self.layer_norm2(out1 + ffn_output)

        return out2

# 多头注意力机制定义
class MultiHeadAttention(tf.keras.layers.Layer):
    def __init__(self, d_model, num_heads):
        super(MultiHeadAttention, self).__init__()
        self.num_heads = num_heads
        self.d_model = d_model

        assert d_model % self.num_heads == 0

        self.depth = d_model // self.num_heads

        self.wq = tf.keras.layers.Dense(d_model)
        self.wk = tf.keras.layers.Dense(d_model)
        self.wv = tf.keras.layers.Dense(d_model)

        self.dense = tf.keras.layers.Dense(d_model)

    def split_heads(self, x, batch_size):
        x = tf.reshape(x, (batch_size, -1, self.num_heads, self.depth))
        return tf.transpose(x, perm=[0, 2, 1, 3])

    def call(self, q, k, v, mask):
        batch_size = tf.shape(q)[0]

        q = self.wq(q)
        k = self.wk(k)
        v = self.wv(v)

        q = self.split_heads(q, batch_size)
        k = self.split_heads(k, batch_size)
        v = self.split_heads(v, batch_size)

        scaled_attention, attention_weights = scaled_dot_product_attention(q, k, v, mask)
        scaled_attention = tf.transpose(scaled_attention, perm=[0, 2, 1, 3])
        concat_attention = tf.reshape(scaled_attention, (batch_size, -1, self.d_model))

        output = self.dense(concat_attention)

        return output, attention_weights

# 点式前馈网络定义
def point_wise_feed_forward_network(d_model, dff):
    return tf.keras.Sequential([
        tf.keras.layers.Dense(dff, activation='relu'),
        tf.keras.layers.Dense(d_model)
    ])

# 编码器位置编码定义
def get_angles(pos, i, d_model):
    angle_rates = 1 / np.power(10000, (2 * (i // 2)) / np.float32(d_model))
    return pos * angle_rates

def positional_encoding(position, d_model):
    angle_rads = get_angles(np.arange(position)[:, np.newaxis], np.arange(d_model)[np.newaxis, :], d_model)
    angle_rads[:, 0::2] = np.sin(angle_rads[:, 0::2])
    angle_rads[:, 1::2] = np.cos(angle_rads[:, 1::2])
    pos_encoding = angle_rads[np.newaxis, ...]
    return tf.cast(pos_encoding, dtype=tf.float32)

# 损失函数定义
loss_object = tf.keras.losses.BinaryCrossentropy(from_logits=True)
def loss_function(real, pred):
    mask = tf.math.logical_not(tf.math.equal(real, 0))
    loss_ = loss_object(real, pred)

    mask = tf.cast(mask, dtype=loss_.dtype)
    loss_ *= mask

    return tf.reduce_mean(loss_)

# 评估指标定义
train_loss = tf.keras.metrics.Mean(name='train_loss')
train_accuracy = tf.keras.metrics.BinaryAccuracy(name='train_accuracy')

test_loss = tf.keras.metrics.Mean(name='test_loss')
test_accuracy = tf.keras.metrics.BinaryAccuracy(name='test_accuracy')

# 模型训练
EPOCHS = 10

num_layers = 4
d_model = 128
num_heads = 8
dff = 512
dropout_rate = 0.1

input_vocab_size = encoder.vocab_size
target_vocab_size = 2

transformer = TransformerModel(num_layers, d_model, num_heads, dff, input_vocab_size, target_vocab_size, dropout_rate)

optimizer = tf.keras.optimizers.Adam()

for epoch in range(EPOCHS):
    train_loss.reset_states()
    train_accuracy.reset_states()
    test_loss.reset_states()
    test_accuracy.reset_states()

    for (batch, (input_seq, target)) in enumerate(train_batches):
        input_mask = tf.math.logical_not(tf.math.equal(input_seq, 0))
        target = tf.expand_dims(target, axis=-1)

        with tf.GradientTape() as tape:
            predictions = transformer((input_seq, input_mask), True)
            loss = loss_function(target, predictions)

        gradients = tape.gradient(loss, transformer.trainable_variables)
        optimizer.apply_gradients(zip(gradients, transformer.trainable_variables))

        train_loss(loss)
        train_accuracy(target, predictions)

        if batch % 100 == 0:
            print('Epoch {} Batch {} Train Loss {:.4f} Train Accuracy {:.4f}'.format(
                epoch + 1, batch, train_loss.result(), train_accuracy.result()))

    for (batch, (input_seq, target)) in enumerate(test_batches):
        input_mask = tf.math.logical_not(tf.math.equal(input_seq, 0))
        target = tf.expand_dims(target, axis=-1)

        predictions = transformer((input_seq, input_mask), False)
        loss = loss_function(target, predictions)

        test_loss(loss)
        test_accuracy(target, predictions)

    print('Epoch {} Test Loss {:.4f} Test Accuracy {:.4f}'.format(
        epoch + 1, test_loss.result(), test_accuracy.result()))

这个示例使用Transformer模型来对IMDB电影评论进行情感分析。它使用TensorFlow Datasets中的IMDB数据集，将每个评论进行编码并将其输入到Transformer模型中，以预测评论的情感（正面或负面）。

decoder的key_pos是如何使用，能否提供代码例子

在ChitGPT中，Decoder的key_pos是通过以下方式使用的：

首先，我们需要在Decoder的初始化函数中定义key_pos：

class Decoder(nn.Module):
    def __init__(self, num_layers, d_model, num_heads, dff, vocab_size, max_seq_len, rate=0.1):
        super(Decoder, self).__init__()
        self.d_model = d_model
        self.num_layers = num_layers
        
        self.embedding = nn.Embedding(vocab_size, d_model)
        self.pos_encoding = positional_encoding(max_seq_len, d_model)
        
        self.dec_layers = [DecoderLayer(d_model, num_heads, dff, rate) for _ in range(num_layers)]
        self.dropout = nn.Dropout(rate)
        self.final_layer_norm = nn.LayerNorm(d_model)
        
        # Define key_pos
        self.key_pos = torch.arange(0, max_seq_len, dtype=torch.long).unsqueeze(0)

    def forward(self, x, enc_output, look_ahead_mask, padding_mask):
        seq_len = x.size(1)
        attention_weights = {}
        
        # Adding embedding and position encoding.
        x = self.embedding(x)  # (batch_size, target_seq_len, d_model)
        x *= torch.sqrt(torch.FloatTensor([self.d_model])).to(x.device)
        x += self.pos_encoding[:, :seq_len, :]
        
        # Applying dropout to the input of the decoder.
        x = self.dropout(x)
        
        for i in range(self.num_layers):
            x, block1, block2 = self.dec_layers[i](x, enc_output, look_ahead_mask, padding_mask)
            
            # Save attention weights
            attention_weights[f'decoder_layer{i+1}_block1'] = block1
            attention_weights[f'decoder_layer{i+1}_block2'] = block2
        
        # Applying a final layer normalization for decoder output.
        x = self.final_layer_norm(x)
        
        return x, attention_weights

然后，在DecoderLayer中，我们可以使用key_pos来计算注意力分数：

class DecoderLayer(nn.Module):
    def __init__(self, d_model, num_heads, dff, rate=0.1):
        super(DecoderLayer, self).__init__()

        self.mha1 = MultiHeadAttention(d_model, num_heads)
        self.mha2 = MultiHeadAttention(d_model, num_heads)

        self.ffn = point_wise_feed_forward_network(d_model, dff)

        self.layer_norm1 = nn.LayerNorm(d_model)
        self.layer_norm2 = nn.LayerNorm(d_model)
        self.layer_norm3 = nn.LayerNorm(d_model)

        self.dropout1 = nn.Dropout(rate)
        self.dropout2 = nn.Dropout(rate)
        self.dropout3 = nn.Dropout(rate)

    def forward(self, x, enc_output, look_ahead_mask, padding_mask):
        # Multi-head attention layer with masking for decoder self-attention
        attn1, block1 = self.mha1(x, x, x, look_ahead_mask)
        attn1 = self.dropout1(attn1)
        out1 = self.layer_norm1(attn1 + x)

        # Multi-head attention layer with padding masking for encoder-decoder attention
        key_pos = self.mha2.decoder_key_pos.unsqueeze(0)
        attn2, block2 = self.mha2(out1, enc_output, enc_output, padding_mask, key_pos=key_pos)
        attn2 = self.dropout2(attn2)
        out2 = self.layer_norm2(attn2 + out1)

        # Point wise feed forward network
        ffn_output = self.ffn(out2)
        ffn_output = self.dropout3(ffn_output)
        out3 = self.layer_norm3(ffn_output + out2)

        return out3, block1, block2

在这个例子中，我们使用 `self.mha2` 来计算Decoder与Encoder之间的注意力，其中 `key_pos` 是 `self.mha2` 中的一个参数，它被设置为 `self.mha2.decoder_key_pos.unsqueeze(0)`，这将 `key_pos` 转换为一个形状为 `(1, max_seq_len)` 的张量，从而与encoder输出的形状相同。在计算注意力分数时，`key_pos` 用于查找encoder输出中每个位置的位置编码，以便在进行注意力计算时使用。