arXiv：cs.LG（机器学习，全量分类）· Yang-yang Tan, Jinyang Li, Lingxiao Wang·· 13 小时前AI 评分49
生成式扩散模型从短时构型对预测随机动力学长期演化
Generative Modeling of Stochastic Dynamics for Long-Time Evolution
AI 导读
生成式扩散模型仅凭固定短时间间隔的构型对即可学习有限时间转移核，无需已知运动方程，迭代该核可将随机动力学推演至远超训练时间尺度。在二维 Model B 中，学到的核复现了动态临界标度与自相似 t^{1/3} 粗化，且在训练最大尺寸两倍的格点和未见初始系综上仍与直接模拟一致。对周期性光势场中的驱动胶体，十分钟实测轨迹即可在实验误差内预测随后二十分钟的粒子流与平均通过时间。
正文
Abstract:Exact stochastic equations for non-equilibrium dynamics are rarely accessible. We show that the long-time evolution of stochastic dynamics can be predicted from configuration pairs at a fixed short time lag, without knowledge of the equation of motion. Generative diffusion models learn the finite-time transition kernel from these pairs, and iterating it propagates the dynamics far beyond the training lag. For two-dimensional Model B, the diffusive dynamics of a conserved order parameter, the learned kernels reproduce dynamic critical scaling and self-similar $t^{1/3}$ coarsening. Agreement with direct simulations persists on lattices twice the largest training size and for initial ensembles absent from training. For driven colloids in a periodic optical potential, ten minutes of measured trajectories suffice to predict the particle current and mean passage time over the next twenty minutes within experimental uncertainty. Short-time observations thus contain the information needed to predict emergent non-equilibrium dynamics at much longer times.
| Comments: | 21 pages, 15 figures, comments are welcome! |
| Subjects: | Statistical Mechanics (cond-mat.stat-mech); Machine Learning (cs.LG); High Energy Physics - Lattice (hep-lat) |
| Report number: | RIKEN-iTHEMS-Report-26 |
| Cite as: | arXiv:2610.00546 [cond-mat.stat-mech] |
| (or arXiv:2610.00546v1 [cond-mat.stat-mech] for this version) | |
| https://doi.org/10.48550/arXiv.2610.00546 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Lingxiao Wang [view email]
[v1]
Wed, 30 Sep 2026 18:26:34 UTC (1,100 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org