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Emulating the First Principles of Matter: A Probabilistic Roadmap
arXiv - CS - Computational Engineering, Finance, and Science Pub Date : 2020-09-30 , DOI: arxiv-2010.05942
Jianzhong Wu, Mengyang Gu

This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the electronic structure and diverse static properties of of many-particle systems useful for practical applications. Pedagogical examples are given to illustrate the basic concepts and simple applications of quantum Monte Carlo and density functional theory -- two representative methods commonly used in the literature of first principles modeling. In addition, this chapter highlights the practical needs for the integration of physics-based modeling and data-science approaches to reduce the computational cost and expand the scope of applicability. A special emphasis is placed on recent developments of statistical surrogate models to emulate first principles calculation from a probabilistic point of view. The probabilistic approach provides an internal assessment of the approximation accuracy of emulation that quantifies the uncertainty in predictions. Various recent advances toward this direction establish a new marriage between Gaussian processes and first principles calculation, with physical properties, such as translational, rotational, and permutation symmetry, naturally encoded in new kernel functions. Finally, it concludes with some prospects on future advances in the field toward faster yet more accurate computation leveraging a synergetic combination {of} novel theoretical concepts and efficient numerical algorithms.

中文翻译:

模拟物质的第一原理:概率路线图

本章提供了描述基态或平衡态物质性质的第一性原理方法的教程概述。它首先简要介绍了量子力学和统计力学,用于预测对实际应用有用的多粒子系统的电子结构和各种静态特性。给出了教学实例来说明量子蒙特卡罗和密度泛函理论的基本概念和简单应用——这两种在第一性原理建模文献中常用的代表性方法。此外,本章强调了将基于物理的建模和数据科学方法相结合以降低计算成本和扩大适用范围的实际需求。特别强调统计代理模型的最新发展,以从概率的角度模拟第一原理计算。概率方法提供了对模拟的近似精度的内部评估,用于量化预测中的不确定性。朝着这个方向的各种最新进展在高斯过程和第一性原理计算之间建立了新的结合,物理特性,如平移、旋转和置换对称性,自然编码在新的核函数中。最后,它总结了该领域未来发展的一些前景,利用新理论概念和有效数值算法的协同组合,实现更快更准确的计算。概率方法提供了对模拟的近似精度的内部评估,用于量化预测中的不确定性。朝着这个方向的各种最新进展在高斯过程和第一性原理计算之间建立了新的结合,物理特性,如平移、旋转和置换对称性,自然编码在新的核函数中。最后,它总结了该领域未来发展的一些前景,利用新理论概念和有效数值算法的协同组合,实现更快更准确的计算。概率方法提供了对模拟的近似精度的内部评估,用于量化预测中的不确定性。朝着这个方向的各种最新进展在高斯过程和第一性原理计算之间建立了新的结合,物理特性,如平移、旋转和置换对称性,自然编码在新的核函数中。最后,它总结了该领域未来发展的一些前景,利用新理论概念和有效数值算法的协同组合,实现更快更准确的计算。和置换对称性,自然编码在新的核函数中。最后,它总结了该领域未来发展的一些前景,利用新理论概念和有效数值算法的协同组合,实现更快更准确的计算。和置换对称性,自然编码在新的核函数中。最后,它总结了该领域未来发展的一些前景,利用新理论概念和有效数值算法的协同组合,实现更快更准确的计算。
更新日期:2020-10-14
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