# ppt_en_template

**Repository Path**: mountain-cat/ppt_en_template

## Basic Information

- **Project Name**: ppt_en_template
- **Description**: No description available
- **Primary Language**: Unknown
- **License**: Not specified
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 0
- **Forks**: 0
- **Created**: 2025-12-01
- **Last Updated**: 2025-12-05

## Categories & Tags

**Categories**: Uncategorized

**Tags**: None

## README

# 英文PPT 模板

https://chat.qwen.ai/c/9f3c0e91-6f09-4ba0-9df2-449fa7b95344


## 一些优化措施


你的**区域划分自适应采样算法（DPAS）**已经有了“分域+残差驱动”的核心思路，这是PINN自适应采样的经典方向之一~可以从**采样效率、划分策略、训练协同、鲁棒性**这几个维度进一步优化，具体建议如下：


### 1. 区域划分策略的优化
当前是“子域残差高于阈值则细分”，可以更灵活：
- **动态划分粒度**：不要固定“细分次数”，而是根据残差的**分布方差**决定划分粒度（比如残差波动大的子域，细分到更小的尺度；残差均匀的子域，保持大尺度），避免过度划分导致采样冗余。
- **多尺度划分融合**：初始用粗粒度划分（比如网格划分），后续结合**聚类算法**（如K-means、GMM）对残差高的区域做“非规则划分”（比如残差的密集区域自动聚合成子域），比规则网格划分更贴合实际残差分布。



### 2. 采样点的筛选效率优化
当前是“生成候选点后直接聚合”，可以增加**采样点的“质量筛选”**：
- **残差加权采样**：生成候选点后，不是全量加入训练集，而是对候选点的残差做**加权抽样**（比如残差大的点被选中的概率更高），避免候选点中“低残差点”占用训练资源。
- **去重/近邻过滤**：对新生成的候选点，和已有训练集做**距离过滤**（比如删除与已有样本距离小于阈值的点），避免采样点过于密集导致训练冗余。



<!-- 不要，不太好 -->
### 3. 与训练过程的协同优化
当前是“采样→更新训练集→M轮训练”，可以让采样和训练更联动：
- **增量训练+采样迭代**：不要等“全部分域采样完成后再训练”，而是采用**“子域采样→小批量训练→再子域采样”**的迭代模式（比如每个子域采样后，先做100轮训练，再处理下一个子域），让模型快速适应新采样点，减少后续残差计算的偏差。
- **动态调整训练轮数M**：根据“新采样点的残差均值”调整M（比如新采样点残差高→增加M轮数；残差低→减少M轮数），避免训练不足或过拟合。





<!-- 这个不要 -->
### 4. 鲁棒性与泛化性优化
- **残差的“置信度加权”**：计算子域残差时，不是用“原始残差值”，而是结合**模型预测的不确定性**（比如蒙特卡洛 dropout 估计的方差），对“低置信度+高残差”的区域优先采样，避免模型对噪声残差的误响应。
- **全局-局部残差的平衡**：当前只关注“子域残差与全局残差的比值”，可以增加**全局残差的“收敛趋势约束”**（比如当全局残差下降到一定阈值后，自动降低细分的阈值），避免后期过度采样。

### 5. 工程实践的优化
- **预训练的“残差初始化”**：预训练阶段可以先做**1-2轮“全局粗采样训练”**，让模型先学习到大致的残差分布，再开始分域采样，避免初始残差计算偏差太大导致划分错误。
- **终止条件的补充**：当前算法没有终止逻辑，可以增加**终止条件**（比如“连续2次采样后，全局残差下降小于阈值”或“训练集规模达到上限”），避免无限迭代。
- **并行计算**:不要遍历每一个子域，太慢，可以对子域并行计算，添加残差点


### 总结
你的DPAS已经抓住了“分域+残差驱动”的核心，优化后可以更贴合PINN的训练特性：既减少冗余采样，又能精准聚焦高残差区域，同时降低训练成本~


Here’s the English version of the optimization suggestions for your DPAS algorithm:


Your **Domain Partition-based Adaptive Sampling (DPAS)** already leverages the core idea of "domain partitioning + residual-driven sampling" — a classic direction for PINN adaptive sampling. You can further optimize it in terms of **sampling efficiency, partitioning strategy, training synergy, and robustness**:


### 1. Optimization of Domain Partitioning Strategy
Currently, you "subdivide a subdomain if its residual exceeds a threshold" — you can make this more flexible:
- **Dynamic Partition Granularity**: Avoid fixing the "number of subdivisions"; instead, determine the partition granularity based on the **variance of residual distribution** (e.g., subdivide subdomains with volatile residuals into smaller scales, while keeping large scales for subdomains with uniform residuals) to reduce redundant sampling from over-partitioning.
- **Multi-scale Partition Fusion**: Start with coarse-grained partitioning (e.g., grid-based), then use **clustering algorithms** (e.g., K-means, GMM) to perform "irregular partitioning" on high-residual regions (e.g., automatically cluster dense residual areas into subdomains). This aligns better with actual residual distributions than regular grid partitioning.


### 2. Optimization of Sampling Point Selection Efficiency
Currently, you "aggregate all candidate points directly" — add **quality filtering for sampling points**:
- **Residual-Weighted Sampling**: After generating candidate points, do not add all of them to the training set. Instead, perform **weighted sampling based on residuals** (e.g., points with larger residuals have higher selection probabilities) to avoid wasting training resources on "low-residual candidates."
- **Deduplication/Nearest-Neighbor Filtering**: For newly generated candidates, apply **distance filtering** against existing training samples (e.g., remove points whose distance to existing samples is below a threshold) to avoid over-dense sampling and training redundancy.


### 3. Synergy Optimization with the Training Process
Currently, the workflow is "sample → update training set → M rounds of training" — make sampling and training more interactive:
- **Incremental Training + Sampling Iteration**: Instead of training *after* all subdomain sampling is complete, adopt an iterative pattern of **"subdomain sampling → small-batch training → next subdomain sampling"** (e.g., after sampling one subdomain, train for 100 epochs before processing the next). This lets the model quickly adapt to new samples and reduces bias in subsequent residual calculations.
- **Dynamically Adjust Training Rounds (M)**: Adjust M based on the **mean residual of new sampling points** (e.g., increase M if new points have high residuals; decrease M if residuals are low) to avoid under-training or overfitting.


### 4. Robustness and Generalization Optimization
- **Confidence-Weighted Residuals**: When calculating subdomain residuals, use **model prediction uncertainty** (e.g., variance estimated via Monte Carlo dropout) instead of raw residual values. Prioritize sampling regions with "low confidence + high residuals" to avoid the model overreacting to noisy residuals.
- **Global-Local Residual Balance**: Currently, you only focus on the "ratio of subdomain residual to global residual." Add a **convergence trend constraint for global residuals** (e.g., automatically lower the subdivision threshold once the global residual drops to a certain level) to avoid over-sampling in later stages.


### 5. Engineering Practice Optimization
- **Residual Initialization in Pre-training**: In the pre-training phase, first perform **1–2 rounds of "global coarse-sampling training"** to let the model learn a rough residual distribution before starting domain partitioning. This reduces partitioning errors caused by large initial residual calculation biases.
- **Add Termination Conditions**: Your current algorithm lacks termination logic. Add conditions like *"global residual drop < threshold for 2 consecutive sampling rounds"* or *"training set size reaches upper limit"* to avoid infinite iteration.


In summary, your DPAS already captures the core of "domain partitioning + residual-driven sampling." These optimizations will make it more aligned with PINN training characteristics: reducing redundant sampling, focusing precisely on high-residual regions, and lowering training costs.



## 参考文献

先配置settings,然后终端执行：

```
biber main # main表示main.tex
```

然后使用xelatex编译