Dexuan Zhou, Huajie Chen, Cheuk Hin Ho, Christoph Ortner
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A Multilevel Method for Many-Electron Schrödinger Equations Based on the Atomic Cluster Expansion
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A105-A129, February 2024. Abstract. The atomic cluster expansion (ACE) [R. Drautz, Phys. Rev. B, 99 (2019), 014104] yields a highly efficient and interpretable parameterization of symmetric polynomials that has achieved great success in modelling properties of many-particle systems. In the present work we extend the practical applicability of the ACE framework to the computation of many-electron wave functions. To that end, we develop a customized variational Monte Carlo algorithm that exploits the sparsity and hierarchical properties of ACE wave functions. We demonstrate the feasibility on a range of proof-of-concept applications to one-dimensional systems.
期刊介绍：
The purpose of SIAM Journal on Scientific Computing (SISC) is to advance computational methods for solving scientific and engineering problems.
SISC papers are classified into three categories:
1. Methods and Algorithms for Scientific Computing: Papers in this category may include theoretical analysis, provided that the relevance to applications in science and engineering is demonstrated. They should contain meaningful computational results and theoretical results or strong heuristics supporting the performance of new algorithms.
2. Computational Methods in Science and Engineering: Papers in this section will typically describe novel methodologies for solving a specific problem in computational science or engineering. They should contain enough information about the application to orient other computational scientists but should omit details of interest mainly to the applications specialist.
3. Software and High-Performance Computing: Papers in this category should concern the novel design and development of computational methods and high-quality software, parallel algorithms, high-performance computing issues, new architectures, data analysis, or visualization. The primary focus should be on computational methods that have potentially large impact for an important class of scientific or engineering problems.
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