Our knowledge of the fundamental particles of nature and their interactions is summarized by the standard model of particle physics. Advancing our understanding in this field has required experiments that operate at ever higher energies and intensities, which produce extremely large and information-rich data samples. The use of machine-learning techniques is revolutionizing how we interpret these data samples, greatly increasing the discovery potential of present and future experiments. Here we summarize the challenges and opportunities that come with the use of machine learning at the frontiers of particle physics. T he standard model of particle physics is supported by an abundance of experimental evidence, yet we know that it cannot be a complete theory of nature because, for example, it cannot incorporate gravity or explain dark matter. Furthermore, many properties of known particles, including neutrinos and the Higgs boson, have not yet been determined experimentally, and the way in which the emergent properties of complex systems of fundamental particles arise from the underlying standard-model theory remains unknown. Many known particles were discovered using detectors that made subatomic particles visible to the human eye. For example, bubble chambers 1 filled with superheated liquids that boil when charged particles pass through them transform the paths of the particles into visible tracks of bubbles, which can then be photographed and analysed. The detectors at the Large Hadron Collider (LHC) 2 are much more complex and record data at far greater rates than is possible using bubble chambers. For example, the LHCb experiment 3 analyses as many events every six seconds as the Big European Bubble Chamber recorded in its entire 11 years of operation (1973)(1974)(1975)(1976)(1977)(1978)(1979)(1980)(1981)(1982)(1983), and the datasets collected by the ATLAS 4 and CMS 5 experiments at the LHC are comparable to the largest industrial data samples. It is impossible for humans to visually inspect such large amounts of data; algorithms running on large computing farms took over this task long ago. Over the past two decades, particle physics has been migrating towards the use of machine-learning methods in the collection and analysis of its large data samples 6 . Pioneering studies that used neural networks 7,8 and boosted decision trees (BDTs) 9,10 in previous-generation experiments [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] laid the groundwork for the emergence of machine learning as an essential tool at the LHC. Machine-learning algorithms made important contributions to the discovery of the Higgs boson 23, 24 and most data-analysis tasks now benefit from the use of machine learning. In parallel, the field of machine learning has developed at a rapid pace and, in particular, the subfield of deep learning has delivered superhuman performance in several domains 25, 26 . Incorporating these tools while maintaining scientific rigour required in particle-physics analyses presents new challenges. This Review focuses on the application and development of machine-learning methods at the LHC, including recent advances based on deep learning. In addition, we present some example applications of deep learning within the subfield of neutrino physics, in which state-of-the-art methods, such as from computer vision, are naturally applicable. The sensor arrays of the LHC experiments produce data at a rate of about one petabyte per second. Even after drastic data reduction by the custom-built electronics used to readout the sensor arrays, which involves zero suppression of the sparse data streams and the use of various custom compression algorithms, the data rates are still too large to store the data indefinitely-as much as 50 terabytes per second, resulting in as much data every hour as Facebook collects globally in a year 27 . In this section we first motivate why it is necessary to produce such immense data samples, before discussing how machine learning is being used to more effectively select-in real time-which data to keep for further studies and which data to permanently discard. In addition, we show how the use of machine learning is leading to more efficient processing of these data using vast computing resources distributed around the world. Both of these big-data challenges must be overcome before the LHC data can be used to advance our knowledge of fundamental particles. Einstein famously related mass m to energy E via E = mc 2 , where c is the speed of light in a vacuum. A powerful particle accelerator such as the LHC, which is 27 km in circumference, is therefore required to create particles orders of magnitude more massive than the proton, such as the Higgs boson. A Higgs boson is produced only once every few billion proton-proton collisions at the LHC. Many other interesting reactions occur orders of magnitude less often. To enable such data samples to be recorded in a reasonable time frame, the LHC collides nearly one billion protons per second. High-energy collisions can produce hundreds of particles, and disentangling such complex events requires detectors with large and diverse sensor arrays. The ATLAS and CMS detectors each contain roughly 100 million detection elements. Most of the particles produced in the LHC experiments decay before they can be detected by any of the sensors. Therefore, LHC analyses must infer what the underlying reactions were on the basis of the properties of the particles that are detected. A wide variety of sensor technologies are used in the LHC detectors. The various signals from the particles that are detected by these sensor arrays are digitized, converting the physical processes involving subatomic particles into large collections of bytes.
Several domains could benefit from the approach we present in this paper, but its best application is probably in physical experiments REF .
Machine learning at the energy and intensity frontiers of particle physics
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Computer Science Medicine