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一个包含数十万甚至上百万个方程的物理模型，被压缩到仅仅4个方程，这完全超乎想象。然而，这正是一个人工智能完成的“壮举”。 seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;"> seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;">近日，物理学家利用人工智能，已经将一个令人生畏的量子问题，“压缩”成了一个只有四个方程的小任务，并且没有牺牲准确性。它有望彻底改变科学家研究包含大量相互作用电子的系统的方式。 seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;"> seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;">此外，如果这种方法可以进一步扩展到其他问题，还有可能帮助设计出具有某些特性的材料，比如超导性，也就是电子在材料中无阻力地流动。论文已于近日发表在《物理评论快报》上。 seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;"> seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px; font-size: 20px !important;">哈伯德模型 seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;"> seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;">这个艰巨的问题涉及电子在网格状格上移动时的行为。当两个电子占据同一个格座时，它们会发生相互作用。这种设置被称为哈伯德模型。 seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;"> seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;">20世纪中期，哈伯德模型是为了解释过渡金属seline; background: transparent; box-sizing: border-box; color: rgb(153, 153, 153) !important;">（比如铁和镍）的巡游铁磁性而引入的，但在过去的50年中，它的意义已经远远超出了最初的范畴。它成了几类重要材料的理想化模型，让科学家能够了解电子行为如何产生人们所追求的物质相，比如超导。这种模型还可以作为新方法的试验场，在它们被用于更复杂的量子系统之前进行测试。 seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;"> seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;">但seline; background: transparent; box-sizing: border-box;">哈伯德模型的关键问题在于，它看似简单，实则不然。即使是电子数量不多，且使用的计算方法是最先进的情况，也需要耗费大量算力。 seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;"> seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;">这是因为，当电子发生相互作用时，它们的“命运”会在量子力学层面上纠缠。这意味着，即使它们在不同格座上相距甚远，这两个电子也不能被单独处理，因此，物理学家不得不同时处理所有电子，而不能一次一个地攻克。随着电子数量增加，更多纠缠显现，计算难度就会呈指数级增加。 seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;"> seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px; font-size: 20px !important;">重正化群 seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;"> seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;">研究量子系统的一种方法是使用所谓的重正化群。这是物理学家掌握的一种数学工具，用来研究一个系统的行为seline; background: transparent; box-sizing: border-box; color: rgb(153, 153, 153) !important;">（比如哈伯德模型）在改变温度等属性，或者在不同尺度上观察属性时如何变化。 seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;"> seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;">不幸的是，一个一直追踪电子之间所有可能的耦合、且不牺牲任何准确性的重正化群，可能包含数万、数十万甚至数百万个需要解的独立方程。除此之外，这些方程还都相当棘手，每个方程都代表了一对电子的相互作用。 seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;"> seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;">研究团队想到了人工智能，他们想要知道，是否可以使用一种被称为神经网络的机器学习工具，让重正化群更易于掌握。 seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;"> seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;">seline; background: transparent; box-sizing: border-box;">神经网络本质上可以看作一台有能力发现隐藏模式的机器。研究团队开始研究这个由十万个耦合在一起的微分方程组成的庞大对象。 seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;"> seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;">首先，机器学习程序会在全尺寸的重正化群内创建连接。接着，神经网络会调整这些连接的强度，直到它找到一个小的方程组，这个小方程组可以产生与原始的、大尺寸的重正化群相同的解。 seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;"> seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;">直到最后，这个程序的输出能够描述哈伯德模型的物理学，而只需4个方程。 seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;"> seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px; font-size: 20px !important;">拓展更多可能 seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;"> seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;">这个结果大大出乎了研究人员的意料，这也意味着他们真的能够借助AI捕捉到相关的物理学。 seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;"> seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;">训练机器学习程序需要大量算力，这个程序运行了整整几个星期。但好消息是，在经过训练之后，现在这个程序还可以被调整来处理其他问题，而不必从头开始。此外，研究团队还调查了这个机器学习究竟“学习”了有关这个系统的哪些知识，这也将有机会为那些难住了物理学家的问题带来新的见解。 seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;"> seline; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; box-sizing: border-box; overflow-wrap: break-word; font-size: 16px; color: rgb(39, 40, 45); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", Arial, sans-serif; letter-spacing: 0.7px; text-indent: 0px;">对科学家而言，最大的开放性问题是这种新方法在更复杂的量子系统中的效果如何，比如电子会进行长程相互作用的材料。他们同样期待，在处理重正化群的其他领域使用这种技术的令人兴奋的可能性，包括复杂的宇宙学和神经科学。
