We present a consensus-based framework that unifies phase space exploration with posterior-residual-based adaptive sampling for surrogate construction in high-dimensional energy landscapes. Unlike standard approximation tasks where sampling points can be freely queried, physical systems with complex energy landscapes such as molecular dynamics (MD) do not have direct access to arbitrary sampling regions due to the physical constraints and energy barriers; the surrogate construction further relies on the dynamical exploration of phase space, posing a significant numerical challenge. We formulate the problem as a minimax optimization that jointly adapts both the surrogate approximation and residual-enhanced sampling. The construction of free energy surfaces (FESs) for high-dimensional collective variables (CVs) of MD systems is used as a motivating example to illustrate the essential idea. Specifically, the maximization step establishes a stochastic interacting particle system to impose adaptive sampling through both exploitation of a Laplace approximation of the max-residual region and exploration of uncharted phase space via temperature control. The minimization step updates the FES surrogate with the new sample set. Numerical results demonstrate the effectiveness of the present approach for biomolecular systems with up to 30 CVs. While we focus on the FES construction, the developed framework is general for efficient surrogate construction for complex systems with high-dimensional energy landscapes.

翻译：我们提出一种基于共识的框架，将相空间探索与基于后验残差的自适应采样统一起来，用于高维能量景观中的代理模型构建。与可自由查询采样点的标准逼近任务不同，具有复杂能量景观（如分子动力学，MD）的物理系统因物理约束和能量势垒而无法直接访问任意采样区域；代理模型的构建进一步依赖于相空间的动力学探索，这带来了重大的数值挑战。我们将该问题表述为一种极小极大优化，共同调整代理逼近与残差增强采样。以MD系统中高维集体变量（CVs）的自由能曲面（FESs）构建作为激励性示例，阐述基本思想。具体而言，最大化步骤建立了一个随机相互作用粒子系统，通过利用最大残差区域的拉普拉斯逼近进行开发，以及通过温度控制探索未知相空间，实现自适应采样。最小化步骤则利用新样本集更新FES代理模型。数值结果表明，该方法对含有多达30个CV的生物分子系统具有有效性。尽管我们聚焦于FES构建，但所提框架对于具有高维能量景观的复杂系统的代理模型高效构建具有通用性。