用高斯过程和自编码器构建核密度泛函理论的替代模型
Building Surrogate Models of Nuclear Density Functional Theory with Gaussian Processesand Autoencoders
AI总结：
本文回顾了将监督和无监督机器学习技术应用于核密度泛函理论的方法，旨在加速构建DFT波函数基组，以应对核性质预测中的巨大计算挑战。
摘要：
从最轻的氢同位素到最近合成的鿫（Z=118），据估计自然界中可能存在的原子核多达约3000种。这些原子核中的大多数寿命极短，无法在地球上存在，但它们在诸如超新星爆炸或中子星合并等天体物理事件中扮演着至关重要的角色，这些事件被认为是宇宙中大多数重元素的起源。由于在测量这些转瞬即逝的物体的感兴趣性质时存在实验困难，以及模拟强相互作用的量子多体系统所涉及的理论和计算问题，理解整个核素图上原子核的结构、反应和衰变是一项巨大的挑战。核密度泛函理论（DFT）是一个完全微观的理论框架，有潜力为核素图中的每个原子核提供这种定量精确的核性质描述。得益于高性能计算设施，它已被成功应用于预测核质量、放射性衰变的全局模式（如β或γ衰变），以及核裂变过程的若干方面，例如自发裂变半衰期。然而，对核谱学或核裂变的预测性模拟，或对理论不确定性的量化及其在应用中的传播，将需要比目前可能的多出几个数量级的计算量。然而，大部分计算工作将花费在生成合适的DFT波函数基组上。这一任务有可能通过借鉴机器学习和人工智能领域的工具而得到显著加速。在本文中，我们回顾了将监督和无监督学习技术应用于核DFT的不同方法。
英文摘要：
From the lightest Hydrogen isotopes up to the recently synthesized Oganesson (Z=118), it is estimated that as many as about 3000 atomic nuclei could exist in nature. Most of these nuclei are too short-lived to be occurring on Earth, but they play an essential role in astrophysical events such as supernova explosions or neutron star mergers that are presumed to be at the origin of most heavy elements in the Universe. Understanding the structure, reactions, and decays of nuclei across the entire chart of nuclides is an enormous challenge because of the experimental difficulties in measuring properties of interest in such fleeting objects and the theoretical and computational issues of simulating strongly-interacting quantum many-body systems. Nuclear density functional theory (DFT) is a fully microscopic theoretical framework which has the potential of providing such a quantitatively accurate description of nuclear properties for every nucleus in the chart of nuclides. Thanks to high-performance computing facilities, it has already been successfully applied to predict nuclear masses, global patterns of radioactive decay like $β$ or $γ$ decay, and several aspects of the nuclear fission process such as, e.g., spontaneous fission half-lives. Yet, predictive simulations of nuclear spectroscopy or of nuclear fission, or the quantification of theoretical uncertainties and their propagation to applications, would require several orders of magnitude more calculations than currently possible. However, most of this computational effort would be spent into generating a suitable basis of DFT wavefunctions. Such a task could potentially be considerably accelerated by borrowing tools from the field of machine learning and artificial intelligence. In this paper, we review different approaches to applying supervised and unsupervised learning techniques to nuclear DFT.
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