Artificial Intelligence Solves Schr?dinger Equation For Molecules¹人工智能解决了Schr?dinger分子方程

The Schr?dinger Equation is a crucial formalism at the center of quantum mechanics. It is used to work out how quantum systems are, and how they evolve. It is also very much a challenge to solve precisely² for a system made of more than a few particles, with approximations use in most cases.

Schr?dinger方程是量子力学中心的一个重要形式主义。它被用来研究量子系统是怎样的，以及它们是怎样进化的。对于一个由多个粒子组成的系统来说，精确地求解也是一个很大的挑战，在大多数情况下使用近似方法。

Computational methods are used to solve the equation for many systems, and a new study published in Nature Chemistry has put forward a new method. The approach, called PauliNet, is a deep neural³ network that can get the exact solution for the equation for molecules with up to 30 electrons.

计算方法被用于求解许多系统的方程，一项发表在《自然化学》杂志上的新研究提出了一种新方法。这种方法被称为PauliNet，是一种深度神经网络，它可以得到含有多达30个电子的分子方程的精确解。

This AI is based on the Monte Carlo method, which uses random⁴ sampling to deliver numerical results of a mathematical function. This particular version was built with the knowledge of physical laws, including the important Pauli exclusion⁵ principle. The algorithm is named after this law.

该人工智能基于蒙特卡罗方法，该方法使用随机抽样来提供数学函数的数值结果。这个特殊的版本是建立在物理定律的知识，包括重要的泡利不相容原理。该算法就是根据这个规律命名的。

Solving the equation can provide insights into the formation and behavior of molecules that several of the current methods can’t provide. This has often been too laborious⁶ to be worth it, hence why this method could be a game-changer.

解出这个方程可以让我们对分子的形成和行为有更深入的了解，这是目前许多方法所不能提供的。这通常过于费力，不值得，因此这一方法可以改变游戏规则。

Dr Alfredo Carpineti

"Escaping the usual trade-off between accuracy and computational cost is the highest achievement in quantum chemistry," lead author Dr. Jan Hermann of Freie Universit?t Berlin, said in a statement. "As yet, the most popular such outlier is the extremely cost-effective density⁷ functional⁸ theory. We believe that deep 'Quantum Monte Carlo,' the approach we are proposing, could be equally, if not more successful. It offers unprecedented⁹ accuracy at a still acceptable computational cost."“摆脱精确度和计算成本之间的通常平衡，是量子化学领域的最高成就，”Freie Universit?t Berlin的首席作者Jan Hermann博士在一份声明中说。到目前为止，最流行的异常值是极具成本效益的密度泛函理论。我们相信，我们正在提出的深度“量子蒙特卡洛”方法，即使不能取得更大的成功，也可以取得同样的效果。它提供了前所未有的准确性，但计算成本仍然可以接受。”

PauliNet allows for a solution of the Schr?dinger Equation to be found for arbitrary molecules. The versatility¹⁰ and strong physical backbone¹¹ of the software deliver these results. The equation is a mathematical description of the quantum state known as the wave function, and translating this wave function for many electrons into a computer language was not easy.

PauliNet允许为任意分子找到Schr?dinger方程的解。软件的多功能性和强大的物理主干提供了这些结果。这个方程是量子态波函数的数学描述，把这个波函数翻译成计算机语言并不容易。

"Instead of the standard approach of composing the wave function from relatively¹² simple mathematical components¹³, we designed an artificial neural network capable of learning the complex patterns of how electrons are located around the nuclei," added Professor Frank Noé, who led the team effort.

“我们设计了一种人工神经网络，能够学习电子在原子核周围位置的复杂模式，而不是用相对简单的数学成分组成波函数的标准方法，”领导该团队的Frank Noé教授补充道。

There are still many kinks to iron out, but the researchers are excited about the possibilities of this algorithm.

还有许多问题需要解决，但研究人员对这种算法的可能性感到兴奋。

"This is still fundamental research," the authors agree, "but it is a fresh approach to an age-old problem in the molecular¹⁴ and material sciences, and we are excited about the possibilities it opens up."“这仍然是基础研究，”作者们表示同意，“但它是分子和材料科学中一个古老问题的新方法，我们对它所带来的可能性感到兴奋。”