发表机构
Shanghai Normal University; Shanghai Jiao Tong University（上海师范大学; 上海交通大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种结合算子学习与流方法的摊销神经采样器，通过映射SDE系数至不变测度实现高效采样，在慢混合和高维场景下显著加速并保持精度。
AI 中文摘要
我们提出了一种摊销神经采样器，将算子学习与流方法相结合用于采样。它将SDE系数函数映射到从参考测度到不变测度的前推，从而能够在随机微分方程族中进行高效采样。我们的框架将传统采样成本转移到初始训练阶段，之后新的SDE实例仅需一次编码器传递和几步ODE求解器步骤，与混合时间无关。为了处理高维问题，我们对系数函数使用拉格朗日轨迹传感器，并在架构中使用交叉注意力。我们还从理论上建立了我们框架的表达能力和分辨率不变性。在1D和2D SDE族上的实验表明，在慢混合区域中，与MCMC相比，我们的方法具有竞争力的精度和显著的加速，跨传感器数量的迁移能力，以及在64D相互作用粒子SDE上的演示结果，而传统网格方法在此不可行。
英文摘要
We introduce an amortized neural sampler that combines operator learning with flow methods for sampling. It maps SDE coefficient functions to pushforwards from a reference measure to the invariant measures, enabling efficient sampling across families of stochastic differential equations. Our framework shifts traditional sampling cost to an initial training phase, after which new SDE instances require only one encoder pass and a few ODE solver steps, independent of mixing time. To handle problems in high dimensions, we use Lagrangian trajectory sensors for the coefficient functions and cross attention in the architecture. We also theoretically establish the expressivity and resolution invariance of our framework. Experiments on 1D and 2D SDE families show competitive accuracy with substantial speedups over MCMC in regimes with slow mixing, transfer across sensor counts, and demonstration results on a 64D interacting particle SDE where traditional grid approaches are infeasible.
