用低秩张量格式高效采样玻尔兹曼分布，提升复杂概率模型生成效率。
Sampling from Boltzmann densities with physics informed low-rank formats
- 通过低秩张量列车格式求解连续性方程实现采样
- 结合确定性与随机步骤，有效调整分布各模式权重
- 适合高维概率分布采样，尤其适用于复杂能量空间
本方法通过在低秩张量列车（TT）格式中求解底层连续性方程，高效生成来自未归一化玻尔兹曼密度的样本。受马尔可夫链蒙特卡洛（MCMC）文献中常用退火路径启发，该路径基于能量空间的线性插值。借鉴序贯蒙特卡洛思想，交替执行由TT表示的流场确定性时间步与包含朗之万和重采样步骤的随机步，以调整目标分布各模式的相对权重，并逐步逼近正确路径分布。我们在多个数值实例中展示了该方法的高效性。
原文摘要 · Abstract (English)
Our method proposes the efficient generation of samples from an unnormalized Boltzmann density by solving the underlying continuity equation in the low-rank tensor train (TT) format. It is based on the annealing path commonly used in MCMC literature, which is given by the linear interpolation in the space of energies. Inspired by Sequential Monte Carlo, we alternate between deterministic time steps from the TT representation of the flow field and stochastic steps, which include Langevin and resampling steps. These adjust the relative weights of the different modes of the target distribution and anneal to the correct path distribution. We showcase the efficiency of our method on multiple numerical examples.
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