核物理与多体物理仿真的参数矩阵模型
Parametric Matrix Models for Emulation in Nuclear and Many-Body Physics
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中文总结 AI 辅助
本文介绍核与多体物理仿真现状，提出结合传统约化基方法与现代参数化机器学习的参数矩阵模型（PMMs），开发开源pyPMM包，为相关研究提供高性能、可解释的仿真工具。
中文摘要 AI 辅助
当前核物理与多体物理的进展依赖于求解大规模强关联量子多体问题的能力。随着理论模型日益复杂，其计算难度也不断提升。同时，量化模型预测的不确定性以及将自由参数拟合到实验观测结果，需要对这些计算成本高昂的模型进行反复评估。代理模型——即仿真器——为实现这些目标提供了手段。本文介绍了核物理与多体物理中仿真技术的现状，讨论了当前流行仿真方法的动机、目标、起源及选定示例，分析了诸多方法间的紧密数学关联，以及为优化特定特性或应用所做的权衡。本文的核心工作是参数矩阵模型（PMMs）方法，这是一种结合了传统约化基方法与现代参数化机器学习的仿真及通用机器学习框架。PMMs可根据需要保留或舍弃底层系统的物理信息，不仅性能优异，还具备近乎无与伦比的适应性、可解释性和作为仿真方法的可信度。本文构建了PMMs的形式化数学框架，并提供了该方法应用的实用分步流程。作为本文的一部分，开发了开源pyPMM包，该包允许任何研究人员使用模块化、可扩展且图形处理单元（GPU）优化的代码构建、训练、共享和部署基于PMM的仿真器，本文中的所有PMM示例均使用该包创建。
英文摘要
Progress in nuclear and many-body physics today is predicated on the ability to solve large-scale, strongly correlated quantum many-body problems. As the theoretical models become more sophisticated, they also become more computationally complex. Simultaneously, quantifying uncertainty in model predictions and fitting free parameters to experimental observations requires repeated evaluation of these expensive models. Surrogate models---known as emulators---provide the means of accomplishing these goals. This thesis provides an introduction into the current state of emulation in nuclear and many-body physics. The motivations, goals, and origins of currently popular emulation methods are discussed along with selected examples. We see how many methods are closely mathematically related and how trade-offs are made to optimize specific properties or applications. The central work in this thesis is the method of parametric matrix models (PMMs), an emulation and general machine learning framework which combines aspects of traditional reduced basis method with modern parametric machine learning. PMMs are able to retain as much or as little physical information about the underlying system as desired, yielding not only excellent performance but also nearly unparalleled adaptability, interpretability, and trustworthiness as an emulation method. A formal mathematical framework for PMMs is developed and accompanied by practical step-by-step procedures for the application of the method. As part of this thesis, the open-source pyPMM package was developed. This package enables any researcher to construct, train, share, and deploy PMM-based emulators with modular, extendable, and graphics processing unit (GPU)-optimized code. All PMM examples in this thesis were created using this package.
