機器學習 凝聚態物理

為什么要機器學習？ (Why machine learning?)

Machine learning is one of today’s most rapidly cutting-edge growing fields of research, with unprecedented promises to offer solutions to existing engineering and research problems. The powerful combination of recent development and practical progress of computing architectures has made possible a large number of successful machine learning applications, in various fields such as automated translation, image and voice recognition, or game-?playing. Recent advancements in machine learning and deep learning with important applications in diverse fields such as high energy physics, condensed matter, astronomy [1] or industry have deepen the understanding and further the progress of the field, leading to the recent development of result-?driven techniques and advanced algorithms with specific agenda.

機器學習是當今最Swift發展的前沿研究領域之一，其空前的承諾將為現有的工程和研究問題提供解決方案。 計算架構的最新發展和實際進步的有力結合，使得在自動翻譯，圖像和語音識別或游戲等各個領域中，大量成功的機器學習應用成為可能。 機器學習和深度學習的最新進展以及在高能物理，凝聚態，天文學[1]或工業等各個領域的重要應用已加深了對該領域的理解并進一步發展，從而導致了成果的最新發展。具有特定議程的驅動技術和高級算法。

While traditional computing algorithms are reaching their limits in simulation capabilities and spending computational resources, condensed matter physics and quantum many-body research require alternative techniques of investigation, problem solving, diagnosis and discovery.

盡管傳統的計算算法在仿真能力和計算資源方面正達到其極限，但凝聚態物理和量子多體研究需要替代性的研究，問題解決，診斷和發現技術。

Neural networks and machine learning methods in general, have finally reached the next stage of development after several decades of significant progress in diverse fields of science, industry, and technology. What does this mean for condensed-matter physics? The key question here is: how can industry-standard machine learning algorithms help condensed matter physics research? In particular, machine learning techniques are recently employed for studying classical and quantum many-body tasks encountered in condensed matter, quantum information, and related fields of physics. Some of the existing techniques employed today by machine learning methods may lend themselves in the future to fundamental research, to an extent, with specific focus on condensed matter and quantum many-body physics topics.

經過數十年在科學，工業和技術各個領域的重大進步，神經網絡和機器學習方法終于進入了下一階段的發展。 這對凝聚態物理意味著什么？ 這里的關鍵問題是：行業標準的機器學習算法如何幫助凝聚態物理研究？ 特別是，機器學習技術最近被用于研究在凝聚態，量子信息和相關物理領域中遇到的經典和量子多體任務。 機器學習方法如今采用的某些現有技術將來可能會在一定程度上適合基礎研究，尤其是在凝聚態物質和量子多體物理學方面。

Quantum many-body simulations of recent models such as predicting quantum phase transition or exotic emergent phenomena, while conceptually simple, still require a large number of quantum states, leading to an exponentially large number of parameters and therefore becoming computationally difficult, since the solution time can grow exponentially with the size of the task.

最近模型的量子多體模擬(例如，預測量子相變或奇異現象)雖然在概念上很簡單，但仍需要大量的量子態，從而導致參數數量呈指數級增長，因此由于求解時間的增加，計算變得困難可以隨著任務的大小呈指數增長。

So, why machine learning? Recently, machine learning methods were proven to be extremely useful in diverse areas of condensed matter research, reproducing existing results generated with other techniques with smaller computational cost and less effort. Deep learning also offers a powerful tool to efficiently represent quantum many-body states, including the ground states of many-body Hamiltonians or quantum dynamics states.

那么，為什么要機器學習呢？ 最近，事實證明，機器學習方法在凝聚態研究的各個領域都非常有用，它以較小的計算成本和較少的工作量重現了其他技術產生的現有結果。 深度學習還提供了一個強大的工具，可以有效地表示量子多體狀態，包括多體哈密頓量的基態或量子動力學狀態。

Condensed matter physics studies microscopic scale interactions of all types of matter at quantum and atom levels, describing them in terms of mesoscopic and macroscopic structure and properties. Condensed matter systems are quite difficult to simulate with traditional computational techniques, predicting approximate solutions hard to test. As condensed matter tasks always deal with massive amounts of interacting particles, these problems become well-suited candidates for solving with machine learning methods, due to big data requirements.

凝聚態物理學研究量子和原子級所有類型物質的微觀尺度相互作用，并用介觀和宏觀結構與性質來描述它們。 濃縮物系統很難用傳統的計算技術來模擬，難以預測近似解。 由于凝聚態任務總是要處理大量相互作用的粒子，因此由于大數據需求，這些問題成為解決機器學習方法的合適候選對象。

In the past few years, condensed matter physicists started to employ artificial intelligence techniques and especially machine learning algorithms and neural networks, to recognize patterns in the behavior dynamics of many-body systems. Condensed-matter physics deals with different properties and phases of matter under varying conditions, as well as the behavior of these phases using different laws of physics, especially quantum mechanics. Various constructive connections between these fields can cross-fertilize both machine learning and quantum many-body physics.

在過去的幾年中，凝聚態物理學家開始采用人工智能技術，尤其是機器學習算法和神經網絡，以識別多體系統行為動力學中的模式。 凝聚態物理處理物質在不同條件下的不同性質和相，以及使用不同的物理定律(尤其是量子力學)處理這些相的行為。 這些領域之間的各種建設性聯系可以使機器學習和量子多體物理學交叉應用。

Such methods can be used together with conventional computing algorithms, such as Quantum Monte Carlo algorithms or Tensor networks, like Matrix Product States or MERA, running on supercomputers, for studying collections of particles in a material. Tensor networks are a recent advanced technique that are gaining traction and find new applications in both machine learning (Neural networks, Deep learning) and diverse subfields of physics (MERA, for example) that require identifying and extrapolating patterns from data.

這樣的方法可以與在超級計算機上運行的常規計算算法(例如量子蒙特卡洛算法或Tensor網絡，例如矩陣乘積狀態或MERA)一起使用，以研究材料中的粒子集合。 Tensor網絡是一種最新的先進技術，正在獲得關注并在機器學習(神經網絡，深度學習)和需要識別和推斷數據模式的物理子領域(例如，MERA)中找到新的應用。

There are also several classical computer science optimization problems, such as Boolean satisfiability and the travelling salesman problem, which are significantly difficult, having been framed under the generic umbrella term of NP-hard problems. Most optimization problems can be formulated as the problem of finding the ground state of a classical Ising-like Hamiltonian from many-body theory.

還存在一些經典的計算機科學優化問題，例如布爾可滿足性和旅行商問題，這在NP-hard問題的總括范圍內已非常困難。 可以將大多數優化問題表述為從多體理論中找到經典的類似于Ising的哈密頓量的基態的問題。

Machine learning can find patterns in a black box, as we don’t actually understand how these patterns are detected. Built heavily on statistics, machine learning methods are powerful tools for recognition and search of patterns and regularities in data. With the exponential growth in the volume of data to be transferred, stored or processed, new methods of machine learning become important. The technique of pattern recognition helps detecting arrangements of any potential features or properties that may provide information about a given data set. This is achieved by classifying the data based on the existing knowledge and on the statistical features extracted from different patterns and their representation.

機器學習可以在黑匣子中找到模式，因為我們實際上并不了解如何檢測到這些模式。 機器學習方法以統計學為基礎，是用于識別和搜索數據模式和規律性的強大工具。 隨著要傳輸，存儲或處理的數據量呈指數增長，新的機器學習方法變得越來越重要。 模式識別技術有助于檢測可能提供有關給定數據集信息的任何潛在特征或特性的排列。 這是通過根據現有知識以及從不同模式及其表示中提取的統計特征對數據進行分類來實現的。

解決舊問題的新方法 (New solutions to old problems)

There are numerous applications of machine learning and neural networks in condensed matter physics. Important open questions of fundamental interest in quantum many body systems may find their answers and insights into the powerful shallow or deep learning architectures that exhibit a complexity that scales similar to the quantum many-body problem. Recent work also suggested [2] that machine learning algorithms are similar and have a common denominator with the “renormalization group”, an mathematical apparatus used in particle and condensed matter physics that maps a microscopic picture onto a macroscopic one.

機器學習和神經網絡在凝聚態物理中有許多應用。 量子多體系統中基本感興趣的重要開放性問題可能會找到答案，并深入了解強大的淺層或深度學習體系結構，這些體系結構的復雜性與量子多體問題相似。 最近的工作還建議[2]，機器學習算法與“重新歸一化組”相似，并且具有相同的分母?！爸匦職w一化組”是一種用于粒子和凝聚態物理的數學設備，可將微觀圖片映射到宏觀圖片。

Several approaches that employ supervised, unsupervised and reinforcement learning methods were developed in the recent years [3]. A recent emerging subset of machine learning is deep neural learning or deep neural networks, using neural networks capable of unsupervised learning from data that is unstructured or unlabeled. Examples of such tools are Generative Adversarial Networks, Boltzmann Machines, Variational Autoencoders, and Convolutional Neural Networks [4].

近年來，開發了幾種采用監督，無監督和強化學習方法的方法[3]。 機器學習的最新新興子集是深度神經學習或深度神經網絡，它使用能夠從非結構化或未標記的數據中進行無監督學習的神經網絡。 這樣的工具的例子是生成對抗網絡，玻爾茲曼機，變分自動編碼器和卷積神經網絡[4]。

Notably, Restricted Boltzmann machines (RBMs) stand out as as a versatile tool originated in statistical physics and high predictive power for theoretical condensed matter physics models and quantum information theory simulations. RBMs are, indeed, one of the fundamental techniques of deep learning, with various applications in dimensional reduction, feature extraction, and recommender systems through modeling of probability distributions associated with wide variety of datasets [5].

值得注意的是，受限玻爾茲曼機(RBM)作為一種多功能工具而脫穎而出，它起源于統計物理學和理論凝聚態物理模型和量子信息理論模擬的高預測能力。 實際上，RBM是深度學習的基本技術之一，它通過對與各種數據集相關的概率分布進行建模，在降維，特征提取和推薦系統中具有各種應用[5]。

Strongly correlated quantum many-body physics requires challenging, high-demanding computational resources for the study of the many-body quantum wavefunction, which exhibits an exponentially scaling complexity. High-performance computational tools such as quantum Monte Carlo and density matrix renormalization group (DMRG) methods have been employed in the recent years to solve problems in condensed-matter physics[6] [7] [8], with important connections to quantum information sciences [9] [10], ranging from numerical solutions and quantum simulators of simple models to of thermalization and quantum quenches, and much more.

高度相關的量子多體物理學需要具有挑戰性的，高要求的計算資源來研究多體量子波函數，該函數顯示出指數級的縮放復雜性。 近年來，已使用諸如量子蒙特卡洛和密度矩陣重整化組(DMRG)方法之類的高性能計算工具來解決凝聚態物理中的問題[6] [7] [8]，與量子信息有著重要的聯系?？茖W[9] [10]，范圍從簡單模型的數值解和量子仿真器到熱化和量子猝滅，等等。

A number of efficient algorithms were rigorously developed to quantify and translate RBMs into tensor network states, with the purpose of employing powerful deep learning architectures in future quantum many-body physics research, such as studying the entanglement entropy bound or the area law. Furthermore, RBMs can produce more efficient classical simulations, due to their higher power in representing quantum many-body states [11] with fewer parameters than tensor network states,

為了在未來的量子多體物理學研究中使用強大的深度學習架構，例如研究糾纏熵界或面積定律，我們嚴格開發了許多有效的算法來量化RBM并將其轉換為張量網絡狀態。 此外，RBM可以產生比張量網絡狀態更少的參數，從而具有更高的功率來表示量子多體狀態[11]，因此可以產生更有效的經典模擬，

期待 (Looking forward)

Condensed matter physics community has already taken advantage, diving into recent explorations of existing predictive algorithms underlying machine learning and neural networks, building an impressive consensus among various predictions and similarities between the two sciences, to steer the next steps in the progress of physics. The currently growing mutually beneficial relation between the fields of condensed matter, statistical physics, and machine learning has opened a new window into future approaches, powerful toy models and computational/data analysis methods being migrated towards the theoretical physics community,

凝聚態物理界已經利用了優勢，深入研究了機器學習和神經網絡基礎上現有的預測算法的最新探索，在兩種科學之間的各種預測和相似性之間建立了令人印象深刻的共識，以指導物理學發展的下一步。 凝聚態物質，統計物理學和機器學習領域之間當前日益增長的互利關系為未來的方法，強大的玩具模型和計算/數據分析方法向理論物理學界的遷移打開了新窗口，

The recent predictive, representational and computational power of machine learning in processing and simulating large data sets in quantum many body physics and condensed matter systems, inspired from a range of real-world problems, such as computer vision and natural language processing, offer a successful, compelling high-profile and efficient tool contributing to the advancements of physical sciences and beyond.

機器學習在處理和模擬量子多體物理學和凝聚態系統中的大數據集方面的最新預測，表示和計算能力，受到計算機視覺和自然語言處理等一系列現實問題的啟發， ，引人注目的高效工具，為物理科學及其他學科的發展做出了貢獻。

[1] E Howard, Holographic renormalization with machine learning, arXiv:1803.11056 [physics.gen-ph] (2018) doi

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翻譯自: https://medium.com/swlh/machine-learning-meets-condensed-matter-d63c378843e7

機器學習 凝聚態物理

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