Yan Jiawei, Touchette Hugo, Rotskoff Grant M
Department of Chemistry, Stanford University, Stanford, California 94305, USA.
Department of Mathematical Sciences, Stellenbosch University, Stellenbosch 7600, South Africa.
Phys Rev E. 2022 Feb;105(2-1):024115. doi: 10.1103/PhysRevE.105.024115.
Sampling the collective, dynamical fluctuations that lead to nonequilibrium pattern formation requires probing rare regions of trajectory space. Recent approaches to this problem, based on importance sampling, cloning, and spectral approximations, have yielded significant insight into nonequilibrium systems but tend to scale poorly with the size of the system, especially near dynamical phase transitions. Here we propose a machine learning algorithm that samples rare trajectories and estimates the associated large deviation functions using a many-body control force by leveraging the flexible function representation provided by deep neural networks, importance sampling in trajectory space, and stochastic optimal control theory. We show that this approach scales to hundreds of interacting particles and remains robust at dynamical phase transitions.
对导致非平衡模式形成的集体动态涨落进行采样，需要探测轨迹空间中的稀有区域。基于重要性采样、克隆和频谱近似的该问题近期方法，已对非平衡系统产生了重要见解，但往往随系统规模扩展不佳，尤其是在动态相变附近。在此，我们提出一种机器学习算法，该算法通过利用深度神经网络提供的灵活函数表示、轨迹空间中的重要性采样以及随机最优控制理论，对稀有轨迹进行采样，并使用多体控制力估计相关的大偏差函数。我们表明，这种方法可扩展到数百个相互作用的粒子，并在动态相变处保持稳健。
