vsPAIR通过配对稀疏变分自编码器，实现逆问题的快速解算与可解释不确定性估计。
Variational Sparse Paired Autoencoders (vsPAIR) for Inverse Problems and Uncertainty Quantification
- 采用配对结构，将观测数据与目标量用变分自编码器联合建模。
- 在盲修补、CT重建和热方程初值反演中均实现高精度解算与结构化不确定性输出。
- 适合需要快速推理与可信不确定性的科学计算场景，如医学成像与物理模拟。
逆问题是众多科学与工程领域中的核心挑战，通常涉及从含噪测量中重构隐藏的底层量。许多应用不仅需要点估计，还需可解释的不确定性。在众多场景中，实现快速推理与不确定性估计仍具挑战但极为重要。本文提出变分稀疏配对自编码器（vsPAIR），其架构将标准变分自编码器用于观测数据编码，同时以稀疏变分自编码器编码感兴趣的量（QoI），二者通过学习的潜在映射连接。变分结构支持不确定性估计，配对设计通过锚定QoI表示到干净数据增强可解释性，稀疏编码则通过聚焦信息至可识别因子而非扩散于所有维度，提供结构化表达。我们在盲修补、计算机断层扫描（CT）及热方程初值反演任务上验证该方法，结果表明vsPAIR能有效求解逆问题，并提供可解释且结构化的不确定性估计。
原文摘要 · Abstract (English)
Inverse problems are fundamental to many scientific and engineering disciplines; they arise when one seeks to reconstruct hidden, underlying quantities from noisy measurements. Many applications demand not just point estimates but interpretable uncertainty. Providing fast inference alongside uncertainty estimates remains challenging yet desirable in numerous applications. We propose the Variational Sparse Paired Autoencoder (vsPAIR) to address this challenge. The architecture pairs a standard VAE encoding observations with a sparse VAE encoding quantities of interest (QoI), connected through a learned latent mapping. The variational structure enables uncertainty estimation, the paired architecture encourages interpretability by anchoring QoI representations to clean data, and sparse encodings provide structure by concentrating information into identifiable factors rather than diffusing across all dimensions. To validate the effectiveness of our proposed architecture, we conduct experiments on blind inpainting, computed tomography (CT), and initial-condition inference for the heat equation, demonstrating that vsPAIR is a capable inverse problem solver that can provide interpretable and structured uncertainty estimates.
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