Sampling from rough energy landscapes
Sampling from rough energy landscapes
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DOI：
10.4310/cms.2020.v18.n8.a9
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发表时间：
2019-03
影响因子：
1
通讯作者：
P. Plech'avc;G. Simpson
中科院分区：
文献类型：
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作者：
P. Plech'avc;G. Simpson
我们研究的挑战，从玻尔兹曼分布与多尺度能源景观采样。多尺度的功能，或“粗糙度”，对应于高度振荡，但有界，扰动的一个光滑的景观。通过数值实验和分析，我们证明了大都会调整Langevin算法的性能可以严重衰减粗糙度的增加。相反，我们证明了随机游走大都会是不敏感的粗糙度。我们还制定了两个替代的采样策略，结合大规模的能源景观的功能，同时抵抗细尺度粗糙度的影响，这些也优于随机游走大都会。这些景观的数值实验证实了我们的预测。开放性问题和数字挑战也得到了强调。
We examine challenges to sampling from Boltzmann distributions associated with multiscale energy landscapes. The multiscale features, or "roughness," corresponds to highly oscillatory, but bounded, perturbations of a smooth landscape. Through a combination of numerical experiments and analysis we demonstrate that the performance of Metropolis Adjusted Langevin Algorithm can be severely attenuated as the roughness increases. In contrast, we prove that Random Walk Metropolis is insensitive to such roughness. We also formulate two alternative sampling strategies that incorporate large scale features of the energy landscape, while resisting the impact of fine scale roughness; these also outperform Random Walk Metropolis. Numerical experiments on these landscapes are presented that confirm our predictions. Open questions and numerical challenges are also highlighted.