Computing properties of molecular systems rely on estimating expectations of the (unnormalized) Boltzmann distribution. Molecular dynamics (MD) is a broadly adopted technique to approximate such quantities. However, stable simulations rely on very small integration time-steps ($10^{-15}\,\mathrm{s}$), whereas convergence of some moments, e.g. binding free energy or rates, might rely on sampling processes on time-scales as long as $10^{-1}\, \mathrm{s}$, and these simulations must be repeated for every molecular system independently. Here, we present Implict Transfer Operator (ITO) Learning, a framework to learn surrogates of the simulation process with multiple time-resolutions. We implement ITO with denoising diffusion probabilistic models with a new SE(3) equivariant architecture and show the resulting models can generate self-consistent stochastic dynamics across multiple time-scales, even when the system is only partially observed. Finally, we present a coarse-grained CG-SE3-ITO model which can quantitatively model all-atom molecular dynamics using only coarse molecular representations. As such, ITO provides an important step towards multiple time- and space-resolution acceleration of MD. Code is available at \href{https://github.com/olsson-group/ito}{https://github.com/olsson-group/ito}.

翻译：计算分子系统的性质依赖于对（未归一化）玻尔兹曼分布期望值的估计。分子动力学（MD）是近似此类量的广泛应用技术。然而，稳定的模拟依赖于极小的积分时间步长（$10^{-15}\,\mathrm{s}$），而某些矩（如结合自由能或速率）的收敛可能依赖于$10^{-1}\,\mathrm{s}$时间尺度的采样过程，且这些模拟必须为每个分子系统独立重复。本文提出隐式传递算子（ITO）学习框架，通过多时间分辨率学习模拟过程的代理。我们采用新型SE(3)等变架构去噪扩散概率模型实现ITO，并证明所得模型能够在多时间尺度上生成自洽的随机动力学，即使系统仅被部分观测。最后，我们提出粗粒化CG-SE3-ITO模型，仅使用粗粒分子表示即可定量模拟全原子分子动力学。因此，ITO为MD的多时间-空间分辨率加速迈出了重要一步。代码见\href{https://github.com/olsson-group/ito}{https://github.com/olsson-group/ito}。