用三角形解码器提升条件生成，显著降低低维分布的模拟误差。
Conditional Sampling via Wasserstein Autoencoders and Triangular Transport
- 引入三角形结构解码器，结合潜在变量独立性假设优化条件生成。
- 在低维支撑问题上，相比低秩集合卡尔曼滤波误差大幅下降。
- 适用于需要高精度条件采样的科学计算与逆问题求解场景。
我们提出条件瓦瑟斯坦自编码器（CWAE），一种利用条件变量与条件变量中低维结构的条件模拟框架。核心思想是修改瓦瑟斯坦自编码器，采用（块）三角形解码器，并对潜在变量施加适当的独立性假设。结果表明，该模型既能利用低维结构，又可作为条件模拟的解码器。我们探讨了CWAE的各种理论性质，包括其与条件最优传输问题的联系。还提出了三种替代形式，构成算法的基础架构变体。一系列数值实验表明，在条件分布支撑真正低维的问题中，不同CWAE变体相比低秩集合卡尔曼滤波（LREnKF）实现了显著的近似误差降低。
原文摘要 · Abstract (English)
We present Conditional Wasserstein Autoencoders (CWAEs), a framework for conditional simulation that exploits low-dimensional structure in both the conditioned and the conditioning variables. The key idea is to modify a Wasserstein autoencoder to use a (block-) triangular decoder and impose an appropriate independence assumption on the latent variables. We show that the resulting model gives an autoencoder that can exploit low-dimensional structure while simultaneously the decoder can be used for conditional simulation. We explore various theoretical properties of CWAEs, including their connections to conditional optimal transport (OT) problems. We also present alternative formulations that lead to three architectural variants forming the foundation of our algorithms. We present a series of numerical experiments that demonstrate that our different CWAE variants achieve substantial reductions in approximation error relative to the low-rank ensemble Kalman filter (LREnKF), particularly in problems where the support of the conditional measures is truly low-dimensional.
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