发表机构
Clemson University; Emory University（克莱姆森大学; 埃默里大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对物理系统代理模型分辨率不匹配问题，提出潜变量孪生算子（LTO），利用ConvCNP风格编解码器与潜演化映射，实现任意分辨率查询与时间推进，并在热方程及纳维-斯托克斯等基准上验证了高精度与迁移能力。
AI 中文摘要
部署在真实物理系统上的代理模型很少能看到固定分辨率的数据：传感器配置在不同部署之间可能不同，并且随着传感基础设施的变化可能随时间演变。我们引入了潜变量孪生算子（LTO），这是一种用于时间演化偏微分方程（PDE）的潜空间代理模型，采用卷积条件神经过程（ConvCNP）风格的编码器和解码器，接受包含$N$个任意位置传感器观测的上下文集合，并可在任何分辨率下进行查询。一个学习到的潜演化映射直接在任意时间点之间推进编码状态，将时间演化与观测和查询离散化解耦。我们推导出在准均匀细化下，空间维度$D$中上下文离散化误差的显式$\u200b\u200b\mathcal{O}(N^{-2/(3D)})$速率。我们在二维热方程基准上实证验证了预测的衰减。在时间相关的PDE基准上，LTO在单步比较下实现了强精度，并以固定参数从原始空间分辨率迁移到更粗的空间分辨率。在纳维-斯托克斯方程上，其直接潜演化进一步在较长预测范围内相对于递归评估减少了误差。
英文摘要
Surrogate models deployed on real physical systems rarely see data at fixed resolutions: sensor configurations vary across deployments and may evolve over time as sensing infrastructure changes. We introduce the Latent Twin Operator (LTO), a latent-space surrogate for time-evolving PDEs with a Convolutional Conditional Neural Process (ConvCNP)-style encoder and decoder that accepts a context set of $N$ sensor observations with arbitrary placement and can be queried at any resolution. A learned latent evolution map advances the encoded state directly between arbitrary time points, decoupling temporal evolution from the observation and query discretizations. We derive an explicit $\mathcal{O}(N^{-2/(3D)})$ rate for the context discretization error in spatial dimension $D$ under quasi-uniform refinement. We verify the predicted decay empirically on a 2D heat-equation benchmark. Across time-dependent PDE benchmarks, LTO achieves strong accuracy under one-step comparisons and transfers from native to coarser spatial resolutions with fixed parameters. On Navier--Stokes, its direct latent evolution further reduces error over longer prediction horizons relative to recursive evaluation.
Comments17 pages, 2 figures, 5 tables
