Enhancing energy predictions in multi-atom systems with multiscale topological learning.

Lithium, a key element in high-energy-density batteries such as lithium-ion batteries, plays a crucial role in determining battery performance, safety, and longevity. Understanding how lithium atoms interact in clusters is essential for optimizing these properties. However, the complexity of these interactions grows exponentially as the number of Li atoms increases. While the rise of large models offers promising avenues for predictive accuracy in such multi-atom systems, the limited data available in material science hinders such breakthroughs. To answer the challenge, we present an interpretable topological learning framework designed to enhance the accuracy of energy predictions in multi-atom systems. This study explores the application of Persistent Topological Laplacians (PTLs), a multiscale topological method that effectively captures the intrinsic properties of many-body interactions. By applying PTLs, we offer a comprehensive analysis to uncover persistent topological features and geometric nuances in complex material systems. A dataset of 136 287 lithium clusters was analyzed using the proposed framework, and the results show that the PTL method aligns with traditional many-body theories, demonstrating its efficacy in capturing complex many-body interactions and improving prediction accuracy.