用神经网络直接学习随机微分方程的演化规律，无需数值求解器即可快速采样。
Neural Stochastic Flows: Solver-Free Modelling and Inference for SDE Solutions
- 基于带约束的条件归一化流，直接建模SDE转移概率分布。
- 在大时间间隔下采样速度提升达两个数量级，计算效率显著提高。
- 适用于金融、物理及视频追踪等含噪声不规则时间序列数据建模。
随机微分方程（SDE）适用于建模金融、物理和机器学习中常见的噪声与不规则采样时间序列。传统方法需依赖昂贵的数值求解器才能在任意时间点采样。本文提出神经随机流（NSFs）及其隐变量变体，通过施加结构约束的条件归一化流直接学习（隐变量）SDE转移律，保留随机流的内在性质。该方法支持任意状态间的一次性采样，在大时间跨度下实现高达两个数量级的速度提升。在合成SDE模拟以及真实世界追踪与视频数据上的实验表明，NSFs在保持与数值方法相当的分布精度的同时，大幅降低了任意时间点采样的计算成本。
原文摘要 · Abstract (English)
Stochastic differential equations (SDEs) are well suited to modelling noisy and irregularly sampled time series found in finance, physics, and machine learning. Traditional approaches require costly numerical solvers to sample between arbitrary time points. We introduce Neural Stochastic Flows (NSFs) and their latent variants, which directly learn (latent) SDE transition laws using conditional normalising flows with architectural constraints that preserve properties inherited from stochastic flows. This enables one-shot sampling between arbitrary states and yields up to two orders of magnitude speed-ups at large time gaps. Experiments on synthetic SDE simulations and on real-world tracking and video data show that NSFs maintain distributional accuracy comparable to numerical approaches while dramatically reducing computation for arbitrary time-point sampling.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。