发表机构
The University of Tokyo; RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS); KEK Theory Center, Institute of Particle and Nuclear Studies; Graduate University for Advanced Studies (SOKENDAI)（东京大学; 理化学研究所跨学科理论与数学科学中心（iTHEMS）; 高能加速器研究机构粒子与核科学研究所理论中心; 综合研究大学院大学（SOKENDAI））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出用生成扩散模型从短时间延迟的构型对学习有限时间转移核，迭代预测随机动力学的长时间演化，并在模型B和驱动胶体中验证了其准确性。
AI 中文摘要
非平衡动力学的精确随机方程很少是可解的。我们表明，随机动力学的长时间演化可以从固定短时间延迟的构型对中预测，而无需知道运动方程。生成扩散模型从这些构型对中学习有限时间转移核，并迭代该核将动力学传播到远超训练延迟的时间。对于二维模型B（守恒序参量的扩散动力学），学习到的核重现了动态临界标度和自相似的$t^{1/3}$粗化行为。与直接模拟的一致性在最大训练尺寸两倍的晶格上以及训练中未出现的初始系综中持续存在。对于周期性光势阱中的驱动胶体，十分钟的测量轨迹足以在实验不确定度内预测接下来二十分钟的粒子流和平均通过时间。因此，短时间观测包含了预测更长时间尺度上涌现的非平衡动力学所需的信息。
英文摘要
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.
Comments21 pages, 15 figures, comments are welcome!
