arXiv 新论文提出 KC-Maps：无需轨迹数据学习 SDE 转移核模拟分子动力学
Kolmogorov-Chapman Maps: Trajectory-Free Learning for Simulating Molecular Dynamics
做分子模拟或 SDE 相关研究的朋友可以看看这篇 arXiv 论文：KC-Maps 不用跑长轨迹数据，直接学转移核，一次前向传播替代数百万步积分，在肽分子系统上比经典分子动力学省 GPU 时。
一篇发布于 arXiv 的论文提出 Kolmogorov-Chapman Maps（KC-Maps），用于学习随机微分方程（SDE）的转移核。该方法不依赖长模拟轨迹数据，只需要轨迹无关的边际样本加上已知的漂移和扩散系数。
技术机制上有两个关键设计：一是把边界条件直接编入神经网络架构，二是利用 Kolmogorov-Chapman 方程构造高效的训练目标。给定初始时间和状态，KC-Maps 可以输出该过程积分到任意时刻的分布，对应 SDE 的弱解，从而把大量数值积分步骤摊销到一次神经网络前向传播中。
作者在肽分子系统上验证了方法，实验显示 KC-Maps 学会了整合动力学，且在 GPU-hours 指标上优于经典分子动力学模拟。传统数值积分单步成本低，但要观察到有意义的事件或状态转变往往需要数百万个连续步骤，GPU 利用率低，这正是该方法针对的痛点。
Kolmogorov-Chapman Maps: Trajectory-Free Learning for Simulating Molecular Dynamics
Stochastic differential equations (SDEs) describe stochastic processes across a wide range of scientific domains, including physics, biology, and finance. Although individual numerical integration steps are inexpensive, observing meaningful events or transitions can require millions of sequential steps, resulting in substantial wall-clock simulation time and poor hardware utilization. Deep learning offers an alternative by amortizing many integration steps into a single neural network forward pass, potentially enabling much faster simulation. However, existing supervised approaches typically require long simulated trajectory data, which restricts their applicability. In this work, we introduce Kolmogorov-Chapman Maps (KC-Maps), a method for learning the transition kernel of an SDE that relies only on the trajectory-free marginal samples together with the known drift and diffusion coefficients. Given an initial time and state of a process, KC-Maps models its distribution integrated to any given time, corresponding to the weak solution of the SDE. To recover the correct dynamics, KC-Maps satisfies two key properties: (i) it satisfies the boundary conditions, which we incorporate directly into the neural network architecture, and (ii) it respects the Kolmogorov--Chapman equation, which provides an efficient training objective. We empirically demonstrate that KC-Maps learns to integrate the dynamics of peptide molecular systems and outperforms classical molecular dynamics in terms of GPU-hours.
This report is categorized under AITOP's "Papers" desk. Within our cross-regional analytical framework, it directly maps to AI developer toolchains, coding agents, and engineering workflows. Key entities and technical topics under continuous tracking include Kolmogorov-Chapman Maps, SDE, 分子动力学, 神经网络.
Source attribution: curated from arXiv cs.LG (@Majdi Hassan, Marta Skreta, Dominique Beaini, Kirill Neklyudov).