用元动力学增强离散神经采样，突破高能垒区域探索瓶颈
MetaDNS: Enhancing Exploration in Discrete Neural Samplers via Well-Tempered Metadynamics
- 引入自适应历史依赖偏置势，驱动采样器跨越高能垒区域
- 在伊辛、庞茨及铜金合金等低温测试中准确复现热力学分布
- 相比传统蒙特卡洛方法，采样效率更高，所需偏置步骤更少
从具有多模态和能量屏障的离散分布中采样是机器学习与计算物理的基础问题。近期的离散神经采样器（如MDNS）存在模式坍缩问题，难以采样模态间的高能垒区域，严重影响自由能估计与相变理解。本文提出元动力学离散神经采样器（MetaDNS），将广义元动力学融入离散扩散或自回归采样框架。通过在选定低维坐标上维持自适应、历史依赖的偏置势，MetaDNS可主动探索此前不可达区域，实现标准神经采样器因缺乏高能样本而无法完成的自由能重建。在伊辛模型、庞茨模型及铜金二元合金等低温挑战性基准上，MetaDNS成功复现了热力学分布。相比基于马尔可夫链蒙特卡洛的元动力学方法，MetaDNS在相当的探索效果下仅需更少的偏置沉积步数。
原文摘要 · Abstract (English)
Sampling from discrete distributions with multiple modes and energy barriers is fundamental to machine learning and computational physics. Recent discrete neural samplers like MDNS suffer from mode collapse and fail to sample high-energy barrier regions between modes, which is critical for free energy estimation and understanding phase transitions. We propose Metadynamics Discrete Neural Sampler (MetaDNS), a general framework integrating well-tempered metadynamics into discrete diffusion or autoregressive samplers. By maintaining an adaptive, history-dependent bias potential along selected low-dimensional coordinates, MetaDNS forces exploration of previously inaccessible regions, enabling free energy reconstruction infeasible with standard neural samplers due to a lack of high-energy samples. On challenging low-temperature benchmarks including Ising, Potts, and the copper-gold binary alloy, MetaDNS reproduces the thermodynamic distribution. Compared to MCMC-based metadynamics, MetaDNS also achieves comparable exploration requiring fewer bias deposition steps.
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