Energy landscapes provide a conceptual framework for structure prediction, and a detailed understanding of their topological features is necessary to develop efficient methods for their exploration. The ability to visualize these surfaces is essential, but the high dimensionality of the corresponding configuration spaces makes this visualization difficult. Here, we present stochastic hyperspace embedding and projection (SHEAP), a method for energy landscape visualization inspired by state-of-the-art algorithms for dimensionality reduction through manifold learning, such as $t$-SNE and UMAP. The performance of SHEAP is demonstrated through its application to the energy landscapes of Lennard-Jones clusters, solid-state carbon, and the quaternary system $\mathrm{C}+\mathrm{H}+\mathrm{N}+\mathrm{O}$. It produces meaningful and interpretable low-dimensional representations of these landscapes, reproducing well-known topological features such as funnels and providing fresh insight into their layouts. In particular, an intrinsic low dimensionality in the distribution of local minima across configuration space is revealed.

中文翻译：

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通过流形学习可视化能源景观

能源景观为结构预测提供了一个概念框架，详细了解其拓扑特征对于开发有效的勘探方法是必要的。可视化这些表面的能力是必不可少的，但相应配置空间的高维使这种可视化变得困难。在这里，我们提出了随机超空间嵌入和投影 (SHEAP)，这是一种能源景观可视化方法，其灵感来自于通过流形学习进行降维的最先进算法，例如$吨$-SNE 和 UMAP。SHEAP 的性能通过其在 Lennard-Jones 簇、固态碳和四元系统的能源景观中的应用得到证明$\mathrm{C}+\mathrm{H}+\mathrm{N}+\mathrm{哦}$. 它为这些景观生成有意义且可解释的低维表示，再现众所周知的拓扑特征，例如漏斗，并提供对其布局的全新洞察。特别是，揭示了跨配置空间的局部最小值分布的固有低维性。