发表机构
Westlake University（西湖大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
PMosFM 提出预处理流形匹配框架，通过流形解码器编码约束并利用几何预处理器与协方差变换，实现一步物理约束生成，降低训练和采样成本。
AI 中文摘要
物理约束生成模型旨在生成匹配目标分布并满足规定约束的物理场。然而，施加这些约束通常通过迭代校正增加采样成本，或通过残差优化和轨迹展开增加训练成本。为解决此问题，我们引入了预处理流形一步流匹配（PMosFM），一种用于一步物理约束生成的预处理流形匹配框架。通过在流形解码器中编码约束，PMosFM 学习内在坐标中的传输，无需单独的残差损失或终端残差展开。几何预处理器使用解码器诱导的度量重新缩放坐标，而正则化协方差变换近似白化插值状态输入。有限区间目标将速度监督与物理空间中解码端点的一致性相结合。我们证明精确参数化消除了残差引起的高斯-牛顿曲率，几何和协方差效应在局部条件数界中分离，物理流映射误差界定了端点分布误差。受控消融研究检查条件数，实验评估优化器更新时间和内存占用。在推理时，PMosFM 使用一次神经传输评估后跟物理解码。跨基准的实验表明，与多步基线相比，在相当的物理和分布保真度下，训练和采样时间更低。代码和数据集将公开发布。
英文摘要
Physics-constrained generative models aim to generate physical fields that match a target distribution and satisfy prescribed constraints. However, enforcing these constraints often increases sampling costs through iterative corrections or training costs through residual optimization and trajectory unrolling. To address this issue, we introduce \textbf{P}reconditioned \textbf{M}anifold \textbf{o}ne-\textbf{s}tep \textbf{F}low \textbf{M}atching (\textbf{PMosFM}), a preconditioned manifold matching framework for one-step physics-constrained generation. By encoding constraints in a manifold decoder, PMosFM learns transport in intrinsic coordinates without separate residual losses or terminal residual unrolling. A geometric preconditioner rescales coordinates using the decoder-induced metric, while a regularized covariance transform approximately whitens the interpolation-state inputs. A finite-interval objective couples velocity supervision with consistency between decoded endpoints in physical space. We show that exact parameterization removes residual-induced Gauss--Newton curvature, that geometric and covariance effects separate in a local conditioning bound, and that physical flow-map error bounds endpoint distributional error. Controlled ablations examine conditioning, and experiments evaluate optimizer-update time and memory footprint. At inference, PMosFM uses one neural transport evaluation followed by physical decoding. Experiments across benchmarks show lower training and sampling time than the multi-step baselines at comparable physical and distributional fidelity. Code and datasets will be released publicly.
