提出新型采样方法，显著提升复杂势能场下的收敛速度。
Accelerated sampling using SamAdams variable timesteps and position-adaptive Langevin dynamics
- 采用自适应步长与位置相关摩擦项，动态调节采样过程。
- 在罗森布洛克和穆勒-布朗势函数上提速1.5至3倍。
- 适合高维复杂分布采样，尤其适用于稀疏贝叶斯推断。
我们提出一种基于朗之万动力学的加速采样方法，包含两个互补机制： 1. SamAdams 自适应步长，通过松弛的刚度监测器在相空间的刚性区域自动减小有效积分步长； 2. 位置自适应朗之万（PAL）动力学，在保持经典分布为精确不变测度的前提下，将阻尼力集中于局部力方向。 两者结合形成的SA-PAL方法，使用回文积分器实现每步仅需一次力计算，通过合理安排积分步骤并利用PAL阻尼张量的秩一加标量结构。我们在多个模型问题上测试该方法：罗森布洛克函数、窄熵通道、穆勒-布朗势函数，以及带有稀疏诱导收缩先验的贝叶斯参数化问题。在罗森布洛克和穆勒-布朗势函数上，混合速率提升1.5至3倍；其他例子中效率提升超过一个数量级。
原文摘要 · Abstract (English)
We introduce an accelerated Langevin-based sampling method that is based on two complementary devices: \emph{SamAdams} adaptive timestepping, which automatically shrinks the effective integration step in stiff regions of phase space using a relaxed stiffness monitor, and \emph{position-adaptive Langevin} (PAL) dynamics, which concentrates friction along the local force direction while preserving the canonical distribution as the exact invariant measure. The resulting combined scheme (SA-PAL) is implemented in a palindromic integrator which requires only one force evaluation per iteration through suitable organisation of the integration steps and by exploiting the rank-one-plus-scalar structure of the PAL friction tensor. We test the method on various model problems: the Rosenbrock function, a thin entropic channel, the Mueller-Brown potential, and a Bayesian parameterisation problem with a sparsity-inducing shrinkage prior. On the Rosenbrock and Mueller-Brown potentials mixing rates are improved by 1.5-3 times compared to fixed stepsize integration. Efficiency gains of more than an order of magnitude are documented in the other examples.
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