Welcome to the Ultimate Guide to Hamburg's Landespokal Football
Football enthusiasts and betting aficionados, welcome to your go-to source for everything related to the Hamburg Landespokal. This guide will take you through the intricacies of this exciting football league, offering expert predictions and daily updates on matches. Whether you're a seasoned bettor or new to the scene, you'll find valuable insights and tips here.
Understanding the Hamburg Landespokal
The Hamburg Landespokal is a prestigious regional football competition in Germany, featuring teams from various clubs within the state of Hamburg. It serves as a crucial stepping stone for clubs aiming to compete at higher levels in German football. The tournament is known for its intense matches and serves as a breeding ground for emerging talent.
Why Follow the Hamburg Landespokal?
- Spotting Rising Stars: Many players who later become stars in larger leagues first make their mark in competitions like the Landespokal.
- Thrilling Matches: With passionate local support, each match is an electrifying experience.
- Betting Opportunities: The unpredictability of outcomes makes it a fertile ground for betting enthusiasts.
Daily Match Updates
Stay ahead with our daily updates on every match in the Hamburg Landespokal. Our team provides comprehensive coverage, including match previews, live scores, and post-match analyses. This ensures you never miss out on any action-packed moments from this vibrant competition.
How We Provide Updates
- Precise Timings: Get real-time updates as they happen.
- Detailed Analyses: Understand the nuances of each game with expert commentary.
- User-Friendly Interface: Navigate through updates effortlessly with our intuitive platform.
In addition to match details, we offer insights into team strategies, player performances, and potential game-changing moments. Our goal is to keep you informed and engaged with every twist and turn of the tournament.
Betting Predictions: Expert Insights
Betting on football can be both exciting and challenging. Our experts use advanced analytics and deep knowledge of local teams to provide accurate predictions that can enhance your betting strategy. Here’s how we ensure top-notch predictions:
- Data-Driven Analysis: We leverage historical data and current form to make informed predictions.
- Tactical Insights: Understanding team tactics gives us an edge in predicting outcomes.
- Social Media Trends: Monitoring fan discussions helps gauge public sentiment and potential surprises.
<%end_of_first_paragraph%>
<%section%>
<% h2 %>% How To Make The Most Of Your Betting Experience <% /h2 %>
<% p %>% Making smart bets requires more than just luck; it involves strategic planning and informed decision-making. Here are some tips to enhance your betting experience during the Hamburg Landespokal:<% /p %>
<% ul %>
<% li %>% **Set a Budget:** Determine how much you’re willing to spend before placing any bets.<% /li %>
<% li %>% **Research Thoroughly:** Use our expert analyses along with your own research to make educated bets.<% /li %>
<% li %>% **Diversify Your Bets:** Spread your wagers across different types of bets (e.g., match outcomes, total goals) to manage risk.<% /li %>
<% li %>% **Stay Informed:** Keep up with daily updates and adjust your strategy based on new information.<% /li %>
<% li %>% **Avoid Emotional Betting:** Don’t let personal biases influence your betting decisions.<% /li %>
<% /ul %>
<% p %>By following these guidelines, you can maximize your chances of success while enjoying the thrill of betting during this exciting football season.<% /p %>
<%section%>
<|...more content...|>
<|...more content...|>
<|...more content...|>
<|...more content...|>
<|...more content...|>
<|...more content...|>
<%= h2 %>%% What Sets Us Apart? %%<%= /h2 %>%%
<%= p %>%% At our platform, we pride ourselves on delivering unmatched value through comprehensive coverage of the Hamburg Landespokal. Our unique blend of expert analysis, real-time updates, and community engagement sets us apart from other sources:<%= /p %>%%
<%= ul %>%%
<%= li %>%% **Expert Team:** Our analysts are seasoned professionals with years of experience in football analytics.<%= /li %>%%
<%= li %>%% **Community Interaction:** Engage with fellow fans through forums and social media channels hosted by us.<%= /li %>%%
<%= li %>%% **Exclusive Content:** Access exclusive interviews with players and coaches that aren’t available elsewhere.<%= /li %>%%
<%= li %>%% **Personalized Alerts:** Customize notifications based on teams or matches that interest you most.<%= /li %>%%
<%= li %>%% **User-Friendly Design:** Enjoy an easy-to-navigate platform designed specifically for avid football followers.<%= /l[0]: import numpy as np
[1]: import matplotlib.pyplot as plt
[2]: from scipy.spatial.distance import cdist
[3]: import pandas as pd
[4]: class KMeans:
[5]: def __init__(self):
[6]: self.k = None
[7]: self.x = None
[8]: self.mu = None
[9]: self.z = None
[10]: self.costs = None
[11]: def _initialize(self):
[12]: """
[13]: Initializes mu randomly.
[14]: Returns:
[15]: mu: (n x k) matrix representing initial cluster centroids
[16]: costs: vector containing cost at each iteration
[17]: z: vector containing cluster assignments at each iteration
[18]: """
***** Tag Data *****
ID: 1
description: Initialization method `_initialize` which initializes cluster centroids,
costs vector containing cost at each iteration, and cluster assignments at each
iteration.
start line: 11
end line: 205
dependencies:
- type: Class
name: KMeans
start line: 4
end line: 10
context description: This method is part of the `KMeans` class responsible for initializing
important variables used throughout k-means clustering algorithm.
algorithmic depth: 4
algorithmic depth external: N
obscurity: 4
advanced coding concepts: 4
interesting for students: 5
self contained: N
************
## Challenging Aspects
### Challenging aspects in above code:
1. **Initialization Complexity**: The `_initialize` method must handle multiple aspects such as initializing cluster centroids (`mu`), tracking costs over iterations (`costs`), and assigning clusters (`z`). Each component has specific requirements that need careful consideration.
2. **Handling Dynamic Data**: The initialization should account for dynamic data changes during iterations (e.g., adding/removing points). Ensuring robustness against such changes adds complexity.
3. **Cost Calculation**: Accurately calculating costs at each iteration requires understanding distance metrics (e.g., Euclidean distance) between data points (`x`) and cluster centroids (`mu`). Missteps here could lead to incorrect clustering results.
4. **Cluster Assignment Logic**: Assigning data points (`x`) to clusters based on proximity requires efficient algorithms that minimize computational overhead while maintaining accuracy.
5. **Iteration Management**: Tracking states across multiple iterations adds another layer of complexity—ensuring consistency between `mu`, `costs`, `z`, etc., throughout all iterations.
### Extension:
1. **Dynamic Cluster Adjustment**: Extend functionality so that clusters can dynamically adjust their number based on certain criteria (e.g., minimum points per cluster).
2. **Adaptive Cost Functions**: Implement adaptive cost functions that change depending on certain conditions (e.g., convergence rate).
3. **Handling High-Dimensional Data**: Add support for efficiently handling high-dimensional datasets without significant performance degradation.
4. **Robust Initialization Techniques**: Integrate advanced initialization techniques like k-means++ which improve convergence speed by better initial centroid selection.
5. **Parallel Processing Support**: Allow parts of the algorithm (like distance calculations) to be parallelized for faster execution without compromising correctness.
## Exercise
### Problem Statement:
You are tasked with extending the provided [SNIPPET] codebase by implementing several advanced features tailored specifically towards enhancing its robustness and efficiency under dynamic conditions.
### Requirements:
1. Implement dynamic adjustment logic where clusters can split or merge based on certain thresholds.
2. Develop adaptive cost functions that modify themselves based on convergence rates.
3. Ensure efficient handling of high-dimensional datasets.
4. Integrate k-means++ initialization technique.
5. Implement parallel processing capabilities where appropriate without compromising correctness.
Use Python's standard libraries alongside any necessary third-party libraries like NumPy or SciPy.
### Constraints:
- You must not use external machine learning libraries like scikit-learn directly; however, using them indirectly through NumPy/SciPy operations is allowed.
- Maintain compatibility with existing class structure provided in [SNIPPET].
## Solution
python
import numpy as np
class KMeans:
def __init__(self):
self.k = None # Number of clusters
self.x = None # Data points matrix (n x d)
self.mu = None # Cluster centroids matrix (k x d)
self.z = None # Cluster assignment vector
self.costs = [] # Costs at each iteration
def _initialize(self):
"""
Initializes mu randomly using k-means++ technique,
calculates initial costs & assigns initial clusters.
Returns:
mu : Initial cluster centroids matrix (k x d)
costs : Vector containing cost at each iteration
initialized empty list
append new cost after every iteration
length equals number iterations + initial state
index i contains cost after ith iteration
index -1 contains final cost
index zero contains initial cost
values are non-negative floats
zero when perfect clustering achieved
zero when n == k == d == z == c == one
strictly decreasing sequence until convergence
initially equal variance if random initialization used
initially lower if smart initialization used e.g kmeans++
non-decreasing sequence if no early stopping employed
z : Vector containing cluster assignments at each iteration initialized empty list append new z after every iteration length equals number iterations + initial state index i contains z after ith iteration index -1 contains final z index zero contains initial z values are integers between zero inclusive & k exclusive uniformly distributed if random initialization used values closer together if smart initialization used e.g kmeans++
"""
n_samples, n_features = self.x.shape
# Initialize centroids using k-means++
self.mu = np.zeros((self.k, n_features))
indices = np.random.choice(n_samples)
self.mu[0] = self.x[indices]
closest_dist_sq = np.full(n_samples, np.inf)
for i in range(1, self.k):
dist_sq = np.sum((self.x - self.mu[i-1]) * (self.x - self.mu[i-1]), axis=1)
closest_dist_sq = np.minimum(closest_dist_sq, dist_sq)
probabilities = closest_dist_sq / closest_dist_sq.sum()
cumulative_probabilities = probabilities.cumsum()
r_i = np.random.rand()
indices = np.searchsorted(cumulative_probabilities,r_i)
self.mu[i] = self.x[indices]
# Calculate initial costs & assign clusters using euclidean distance metric
distances_to_centroids= cdist(self.x,self.mu,'euclidean')
def cdist(x,y,p='euclidean'):
#calculates pairwise distance between two matrices using specified metric 'm'
#returns result as matrix 'd' where entry ij represents distance between row i from x & row j from y according metric m
#initialization
#matrix d stores pairwise distances according metric m calculated between rows from x & rows from y dimensions nxm where n=#rows x m=#rows y
d=np.zeros((x.shape(0),y.shape(0)))
#calculate pairwise distances according specified metric 'm'
if p=='euclidean':
for i in range(x.shape(0)):
for j in range(y.shape(0)):
d[i,j]=np.sqrt(np.sum((x[i,:]-y[j,:])**2))
elif p=='manhattan':
for i in range(x.shape(0)):
for j in range(y.shape(0)):
d[i,j]=np.sum(np.abs(x[i,:]-y[j,:]))
elif p=='chebyshev':
for i in range(x.shape(0)):
for j in range(y.shape(0)):
d[i,j]=np.max(np.abs(x[i,:]-y[j,:]))
else:
raise ValueError('Invalid Distance Metric Specified')
return d
def assign_clusters(distances):
#assigns clusters based on minimum distances
assignments=np.argmin(distances,axis=1)
return assignments
def calculate_cost(distances,assignments):
#calculates total clustering cost
cost=np.sum([distances[i,assignments[i]]**2 for i in range(distances.shape(0))])
return cost
def update_centroids(data,assignments,k):
#updates centroid positions
centroids=np.array([data[np.where(assignments==i)].mean(axis=0) for i in range(k)])
return centroids
def check_convergence(old_mu,new_mu,tolerance=1e-4):
#checks whether centroids have converged
converged=np.linalg.norm(old_mu-new_mu)=max_iters:
break
print(f'K-Means converged after {iterations} iterations.')
print(f'Final Cost:{cost}')
print(f'Cluster Assignments:n{kmeans.z}')
print(f'Centroid Positions:n{kmeans.mu}')
## Follow-up Exercise:
### Problem Statement:
Building upon your previous implementation:
1. Modify your algorithm so it supports streaming data—new data points may arrive during execution.
2. Implement a mechanism where if a cluster's size falls below a threshold during an update step due to streaming data removals/additions it either merges with another nearby cluster or splits into smaller sub-clusters dynamically.
### Solution:
The solution would involve integrating mechanisms such as queue handling for incoming data streams along with additional checks within main loop iterations ensuring dynamic adjustments based on evolving dataset characteristics.
Implement a python module according to the following instructions:
## General functionality
The code defines two classes representing different types of neural network layers commonly used within deep learning models for image processing tasks such as object detection or semantic segmentation.
The first class implements a Spatial Pyramid Pooling layer which takes an input feature map tensor from previous convolutional layers and applies pooling operations over different regions defined by predefined spatial bins (grid sizes). The output is then flattened into a single vector per input image regardless of its original size.
The second class implements an Adaptive Average Pooling layer which resizes an input feature map tensor into a fixed size output tensor by applying average pooling over spatial regions determined by predefined grid sizes similar to those used by Spatial Pyramid Pooling but without flattening into vectors.
Both classes are designed to work within TensorFlow's computation graph framework but do not contain actual implementations within their methods; they serve as templates or interfaces that need further implementation details filled out by developers according to specific requirements or model architectures.
## Specifics and edge cases
- Both classes should accept parameters defining grid sizes (`g_s`) which determine how many regions/slices will be created along both height (`H`) and width (`W`) dimensions during pooling operations.
- Both classes should also accept parameters defining kernel sizes (`kernel_sizes`) which determine how many rows/columns will be included within each region/slice created by grid sizes.
- In Spatial Pyramid Pooling layer:
- If no kernel sizes are provided upon instantiation or calling `call`, default kernel sizes should be set such that only one slice covers all rows/columns respectively.
- During pooling operations within `call`, padding should be applied symmetrically around slices if they do not fit perfectly within dimensions defined by grid sizes multiplied by kernel sizes.
- After pooling operations across all regions/slices defined by grid sizes, results should be concatenated along channels dimension followed by flattening into vectors before being stacked together into tensors corresponding to batches present in input tensor `X`.
- In Adaptive Average Pooling layer:
- If no kernel sizes are provided upon instantiation or calling `call`, default kernel sizes should be set such that only one slice covers all rows/columns respectively.
- During pooling operations within `call`, padding should be applied symmetrically around slices if they do not fit perfectly within dimensions defined by grid sizes multiplied by kernel sizes.
- After pooling operations across all regions/slices defined by grid sizes, results should be concatenated along channels dimension without flattening into vectors before being stacked together into tensors corresponding to batches present in input tensor `X`.
## Programmatic aspects
- Use TensorFlow's computation graph capabilities such as placeholders (`tf.placeholder`), reshaping tensors (`tf.reshape`), concatenating tensors along specified axes (`tf.concat`), stacking tensors along batch dimension (`tf.stack`), creating variables (`tf.Variable`), applying padding (`tf.pad`), performing average pooling operations (`tf.nn.avg_pool`).
- Define classes without actual implementations inside methods except placeholders indicating where future logic will reside.
- Use Python lists comprehensions for concise construction of lists needed during padding calculations.
- Utilize control structures like loops (both traditional `for` loops indicated by comments "FOR" instead of "FOR") for iterating over batch elements and grid slices during pooling operations.
## Constants, data and tables
No hard-coded constants other than default values for parameters like `kernel_sizes=None`. These defaults imply behavior when no specific kernel size configuration is provided upon class instantiation or method calls.
python
import tensorflow as tf
class SpatialPyramidPooling(tf.Module):
def __init__(self, g_s=[1], kernel_sizes=None):
super(SpatialPyramidPooling, self).__init__()
self.g_s = g_s
if kernel_sizes is None:
# Default behavior when no specific kernel size configuration is provided upon instantiation.
pass
def call(self, X):
# FOR placeholder indicating future logic implementation location.
class AdaptiveAveragePooling(tf.Module):
def __init__(self, g_s=[1], kernel_sizes=None):
super(AdaptiveAveragePooling).__init__()
self.g_s = g_s
if kernel_sizes is None:
# Default behavior when no specific kernel size configuration is provided upon instantiation.
pass
def call(self, X):
# FOR placeholder indicating future logic implementation location.
User: Can we add support for max pooling operation option besides average pooling?
Assistant:
Certainly! You can extend both classes with an additional parameter called `pooling_type`. Here's how you might modify the constructor (__init__ method) and call method:
python
class SpatialPyramidPooling(tf.Module):
def __init__(self, g_s=[1], kernel_sizes=None, pooling_type='avg'):
super(SpatialPyramidPooling).__init__()
...
Welded Joint Design Optimization Using Deep Learning-Based Generative Adversarial Networks"
authors={Dong Sun,Yang Liu,Zhenyu Li,Ya Zhang,Xiaoqiang Chen,Jian Wang},
journal={International Journal Of Automation Technology},
volume={14},
number={6},
pages={2417--2427},
year={2020},
doi={10.1007/S15066-020-1319-9}
}
@article{hu2019generative,
title={Generative Adversarial Networks Based Training Method For Structural Health Monitoring Of Large Scale Structures},
author={Hu Binbin et al}
}
@article{shao2018deep,
title={Deep learning-based shape optimization via adjoint sensitivity analysis},
author={Shao Jie et al},
journal={AIAA journal},
volume={56},
number={10},
pages={3968--3987}
}
@article{wang2018deep,
title={{Deep} {Learning}-Based Optimal Shape Design Under Uncertainty With Surrogate Models And Sensitivity Analysis Methods},
author={{Wang} {Yanming} et al}
}
@article{chen2018deep,
title={{Deep} {Learning}-Based Optimal Shape Design With Bayesian Optimization And Surrogate Models},
author={{Chen} {Mengqi} et al}
}
@inproceedings{huang2020novel,
title={{Novel} {Generative} {Adversarial} {Network}-{Based} {Methodology} {For} {Optimizing} {Structural} {Design}},
author={{Huang}, Wei-Hsin et al}
}
@article{duan2016unreasonable,
title={{Unreasonable Effectiveness Of Deep Learning In Computational Mechanics}},
author={{Duan}, Yuchao et al}
}
@inproceedings{xu2020data,
title={{Data-driven topology optimization using generative adversarial networks}},
author={{Xu}, Luyang et al}
}
@inproceedings{lai2020generative,
title={{Generative Adversarial Network-Based Topology Optimization For Compliance Minimization}},
author={{Lai}, Bojun et al}
}
@inproceedings{lai20202nd,
title={{A Second Order Generative Adversarial Network-Based Topology Optimization Method For Compliance Minimization}},
author={{Lai}, Bojun et al}
}
@article{mao2019surrogate,
title={{Surrogate model assisted topology optimization using generative adversarial networks}},
author={{Mao}, Zhiqiang et al}
}
@article{shen20201st,
title={"First-order" generative adversarial network-based topology optimization via gradient matching},
author="Shen Huiyi textit{et al}",
journal="Engineering Structures",
volume="211",
pages="110717",
url="https://doi.org/10.1016/j.engstruct.20201.110717"
}
end{thebibliography}<|repo_name|>bojunlai/GAN-TOP<|file_sep>> ## GAN-TOP：基于生成对抗网络的拓扑优化方法（一）：原理、过程及结果分析（英文）
***
**关键词：** 拓扑优化，生成对抗网络，机器学习，深度学习，设计空间探索，结构优化。
本文主要介绍了一种基于生成对抗网络（GAN）的拓扑优化方法。本文首先回顾了GAN的相关知识，并介绍了本文中采用的GAN模型。接下来讨论了GAN在拓扑优化中的应用，并提出了一种新的拓扑优化方法。最后，通过实验分析了本文提出的方法在不同问题上的效果。
#### 前言：
传统拓扑优化通常使用拉格朗日乘数法或者有限元法等计算机辅助设计技术求解目标函数极值点。然而，这些方法需要使用大量计算资源，并且只能处理简单问题。近年来，在结构设计领域越来越多地应用深度学习技术。例如，在《Unreasonable Effectiveness Of Deep Learning In Computational Mechanics》中，作者通过使用神经网络建立目标函数与输入参数之间的映射关系，从而获得比传统有限元法更高效和更准确的目标函数评估方法。但是该方法仅适用于确定性问题，并且需要大量样本数据进行训练。
生成对抗网络（GAN）是一种新型的深度学习模型，在图像处理、图像合成等方面取得了很好的效果。因此，在拓扑优化中引入GAN也可能会获得更好的结果。
#### GAN模型：
生成对抗网络由两个神经网络组成：生成网络（Generator）和判别网络（Discriminator）。生成网络从随机噪声中产生数据样本；判别网络则接收真实数据样本和生成数据样本作为输入，并判断哪些样本为真实数据样本。两个神经网络通过交替训练以达到平衡状态，即判别网络无法区分真实数据与生成数据。
#### GAN-TOP：
在拓扑优化中引入GAN后可以将其视为一个博弈过程：生成器试图找到一个最佳设计以使得目标函数取得最小值；判别器则试图找到一个最佳设计以使得目标函数取得最大值。在这个过程中，两个神经网路都会不断更新自己以达到平衡状态。
具体流程如下：
#### 实验分析：
##### 实验设置：
在以下实验中我们将使用三种不同类型的问题进行测试：圆形孔洞排列、正方形孔洞排列和随机分布孔洞排列。
对于每种类型问题我们将测试三个不同大小尺寸（$N_x times N_y$）：$30times30$、$50times50$和$70times70$。
同时我们还将测试三种不同比例因子$lambda_{{v}}$: $10000$, $20000$, $30000$
每个实验均采用相同参数配置进行训练：
* 批次大小(batch_size)=64；
* 学习率(lr)= $10^{-5}$；
* 训练轮数(epoch)=500；
* 隐层节点数(hiddensize)=128；
* 噪声向量长度(z_size)=100;
* 权重衰减项(weight_decay)= $10^{-5}$;
* 非线性激活函数(non_linear_function)=ReLU;
##### 实验结果：
###### 圆形孔洞排列：
###### 正方形孔洞排列：
###### 随机分布孔洞排列：
从以上结果可以看出，在圆形孔洞排列情况下，当$lambda_{{v}}leq20000$时GANTOP表现良好；而在正方形孔洞排列和随机分布孔洞排列情况下GANTOP无论$lambda_{{v}}$取何值均表现良好。
同时我们还发现当尺寸增加时GANTOP表现更好。
<|repo_name|>bojunlai/GAN-TOP<|file_sep
documentclass[a4paper]{beamer}
usepackage{xcolor,colortbl}% http://ctan.org/pkg/xcolor,colortbl
usepackage[sfdefault]{roboto}% http://ctan.org/pkg/roboto
usepackage[T1]{fontenc}% http://ctan.org/pkg/fontenc
usetheme[]{metropolis}% http://ctan.org/pkg/beamer-theme-metropolis
setbeamertemplate{blocks}[rounded][shadow=true]
title[GANTOP]{基于生成对抗网络\ 的拓扑优化方法}
subtitle{}
date{today{} \ small{}{insertframenumber/inserttotalframenumber}}
author{
Bojun Lai \ texttt{href{mailto:[email protected]}{[email protected]}}
vspace{-15pt}}
%institute{}
%titlegraphic{includegraphics[scale=.25]{logo.pdf}}
%setbeamertemplate{navigation symbols}{}
begin{document}
%maketitle{}
%begin{textblock}{100}(50,-20)
%includegraphics[scale=.25]{logo.pdf}
%end{textblock}
%%%%%%%%%%%%%%% Title Page%%%%%%%%%%%%%%
{
setbeamertemplate{footline}{%
vspace{-20pt}hspace{-40pt}usebeamercolor[named=titlelike]{normal text}{%
normalsize%
Bojun Lai \
[email protected] \
normalsize%
vspace{-15pt}}
}maketitle{}
%%%%%%%%%%%%%%% Title Page End%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
begin{frame}[t]frametitle{}
vspace{-15pt}hspace{-20pt}{
noindentrule{linewidth}{0mm}vspace{-15pt}\[-13pt]
rule{linewidth}{2mm}\[-13pt]
noindentrule{linewidth}{0mm}}
vspace{-35pt}hspace{-40pt}{
normalsize textbf {textcolor<+->{blue!80!black}{$研究背景及动机$}}\[-15pt]}
vspace{-30pt}{
normalsize textbf {textcolor<+->{blue!80!black}{$传统拓扑优化技术缺陷:$}}\[-15pt]}
vspace{-20pt}{
normalsize textbf {textcolor<+->{blue!80!black}{$①计算量大;$}}\[-15pt]}
vspace{-20pt}{
normalsize textbf {textcolor<+->{blue!80!black}{$②可解决问题较少;$}}\[-15pt]}
vspace{-20pt}{
normalsize textbf {textcolor<+->{blue!80!black}{$③受限于用户先验知识;$}}\[-15pt]}
vspace{-30pt}{
normalsize textbf {textcolor<+->{blue!80!black}{$近年来研究:$}}\[-15pt]}
vspace{-20pt}{
normalsize textbf {textcolor<+->{blue!80!black}{$①结合深度学习;$}}\[-15pt]}
vspace{-20pt}{
normalsize textbf {textcolor<+->{blue!80!black}{$②直接搜索;$}}\[-15pt]}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
{
setbeamertemplate{footline}{%
vspace{-20pt}hspace{-40pt}usebeamercolor[named=titlelike]{normal text}{%
normalsize%
Bojun Lai \
[email protected] \
normalsize%
vspace{-15 pt}}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
{
setbeamertemplate{footline}{%
vfill{}vskip-baselineskip{}vskip-baselineskip{}vskip-baselineskip{}%
bgroup%
xdefsavedimageresolution{theimageresolution}% store current resolution setting globally
xdefsavedimagerelief{therelIE}% store current relief setting globally
xdefsavedimagerounding{theRounding}% store current rounding setting globally
xdefsavedimenunitlength{theMENunitlength}% store current unit length setting globally
xdefsavedimenunitsquarewidth{theMENunitsquarewidth}% store current square width setting globally
xdefsavedimenunitdepth{theMENunitdepth}% store current unit depth setting globally
xdefsavedimenunitsquareheight{theMENunitsquareheight}% store current square height setting globally
xeightpointonefalse% force point mode always off globally
%relIEfalse% force relief mode always off globally
%Roundingfalse% force rounding mode always off globally
%imageresolution=maxdimen% set resolution limit infinitely large globally
%MENunitlength=maxdimen% set unit length infinitely large globally
%MENunitsquarewidth=maxdimen% set square width infinitely large globally
%MENunitdepth=maxdimen% set unit depth infinitely
