← 研踪 PaperTrailarXiv:2611.12880 · v1
Kolmogorov-Chapman Maps: Trajectory-Free Learning for Simulating Molecular Dynamics
首次提交 2026-11-10 02:59
版本更新 2026-11-10 02:59
雷达观测 2026-11-10 15:22
摘要
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.
观测到的版本
相邻记录可能跳过中间版本；首次发现 v2 及以上也会标为版本更新。
v1 · 2026-11-10 02:59 · 最新观测版本
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.
查看此版本解读 →查看此版本原文 ↗