Sampling from high-dimensional Gibbs measures poses a challenge when the energy landscape consists of multiple metastable states. Enhanced-sampling methods mitigate this difficulty by introducing adaptive biasing potentials to facilitate the exploration along prescribed collective variables (CVs), but their scalability is often limited by the dimension of the CV space. Motivated by the Wasserstein-gradient-flow interpretation of adaptive biasing, we propose a regularized path-dependent McKean--Vlasov formulation for high-dimensional enhanced sampling. The formulation replaces the variational regularization of the Wasserstein functional by a direct regularization of the CV marginal density in the McKean--Vlasov drift, avoiding the outer convolution over the CV domain. Furthermore, it replaces the instantaneous law by a weighted path-history measure to improve statistical stability in the small-replica regime. We establish well-posedness of the resulting regularized and path-dependent stochastic dynamics under suitable assumptions. For numerical realization, the history-averaged CV marginal density is approximated using an optimization-free functional hierarchical tensor representation, leading to a scalable density-based adaptive biasing scheme. Numerical experiments on benchmark potentials and molecular systems demonstrate the effectiveness of the proposed method for sampling problems with CV dimensions up to 64.

翻译：从高维吉布斯测度中采样面临能量景观包含多个亚稳态的挑战。增强采样方法通过引入自适应偏置势促进沿预设集体变量（CV）的探索来缓解这一困难，但其可扩展性通常受限于CV空间的维度。受自适应偏置的Wasserstein梯度流解释启发，我们提出一种用于高维增强采样的正则化路径依赖McKean–Vlasov模型。该模型将Wasserstein泛函的变分正则化替换为对McKean–Vlasov漂移中CV边缘密度的直接正则化，避免了CV域上的外部卷积。此外，它用加权路径历史测度替代瞬时分布，以改善小副本体系下的统计稳定性。在适当假设下，我们证明了所得正则化路径依赖随机动力学的适定性。数值实现中，历史平均CV边缘密度通过无优化的层次张量表示近似，从而得到可扩展的基于密度的自适应偏置方案。对标势与分子体系的数值实验表明，所提方法在CV维度高达64的采样问题上具有有效性。