Solution of the many-electron Schrödinger equation with deep neural networks

用深度神经网络求解多电子薛定谔方程

• 批准号: 2443624
• 金额: --
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2443624
• 关键词: Solution; many; electron; Schr; dinger

Given access to accurate solutions of the many-electron Schrödinger equation, nearly all chemistry could be derived from first principles. Exact wavefunctions of interesting chemical systems are out of reach because they are NP-hard to compute in general, but approximations can be found using polynomially-scaling algorithms. The key challenge for many of these algorithms is the choice of approximate wavefunction, which must find a balance between efficiency and accuracy. Neural networks have shown impressive power as accurate practical function approximators and promise as a compact approximate wavefunction for spin systems, but problems in electronic structure require wavefunctions that obey Fermi-Dirac statistics. In a very recent preprint (arXiv:1909.02487), we introduced a novel deep learning architecture, the Fermionic Neural Network, as a powerful approximate wavefunction for many-electron systems and showed that this can be combined with the well-known and appealingly simple variational quantum Monte Carlo (VMC) method to achieve accuracy well beyond that achieved in previous VMC simulations atoms and small molecules. Using no data other than atomic positions and charges, we predicted the dissociation curves of the nitrogen molecule and hydrogen chain, two challenging strongly-correlated systems, to significantly higher accuracy than the coupled-cluster method, widely considered the most accurate scalable method for quantum chemistry at equilibrium geometry. This demonstrates that deep neural networks can improve the accuracy of variational quantum Monte Carlo to the point where it outperforms other ab-initio quantum chemistry methods.Mr Cassella's PhD project will build on this promising start by using neural network trial wavefunctions to study simple solids. For simplicity, we will start by looking at the uniform electron gas (which will require substantial code development) before moving on to solid hydrogen and perhaps other simple solids. We will also investigate using fermionic neural networks to improve the accuracy of the more sophisticated diffusion quantum Monte Carlo method.

如果能得到多电子Schrödinger方程的精确解，几乎所有的化学都可以从第一性原理推导出来。有趣的化学系统的精确波函数是无法达到的，因为它们通常是np困难的计算，但可以使用多项式缩放算法找到近似值。这些算法的关键挑战是近似波函数的选择，它必须在效率和精度之间找到平衡。神经网络作为精确实用的函数逼近器已经显示出令人印象深刻的能力，并且有望作为自旋系统的紧凑近似波函数，但电子结构中的问题需要遵从费米-狄拉克统计的波函数。在最近的一篇预印本（arXiv:1909.02487）中，我们介绍了一种新的深度学习架构，费米子神经网络，作为多电子系统的强大近似波函数，并表明它可以与众所周知的、简单的变分量子蒙特卡罗（VMC）方法相结合，以达到远远超过以前VMC模拟原子和小分子所达到的精度。除了原子位置和电荷外，我们没有使用其他数据，我们预测了氮分子和氢链这两个具有挑战性的强相关系统的解离曲线，其精度明显高于被广泛认为是平衡几何量子化学最准确的可扩展方法的耦合簇方法。这表明，深度神经网络可以提高变分量子蒙特卡罗的精度，达到优于其他从头算量子化学方法的程度。Cassella先生的博士项目将以这个有希望的开端为基础，利用神经网络试验波函数来研究简单的固体。为了简单起见，我们将从均匀电子气体开始（这将需要大量的代码开发），然后再转到固体氢和其他简单固体。我们还将研究使用费米子神经网络来提高更复杂的扩散量子蒙特卡罗方法的准确性。