Physicists from the United States have developed a neural network that calculates the height of the beam of synchrotron radiation with an accuracy of about 0.4%, and at the same time is limited by the capacity of a conventional home Computer. Moreover, the neural network advises how to adjust the installation parameters so that the height fluctuations are minimal. Using this algorithm on the real synchrotron ALS, the scientists almost reduced the amplitude of vibrations of the resulting beam (from 1.5 to 0.2 micrometres).
When charged relativistic particles move on circular trajectories in a constant magnetic field, they emit electromagnetic synchrotron radiation. Due to relativistic effects, almost all emitted radiation lies in a narrow cone, the axis of which is directed along with the speed of the particle, and the angle of the solution is inversely proportional gamma factor. Therefore, to an outside observer who looks at the trajectory of the particle, it seems as if the particle emits radiation by narrow flashes with a fixed frequency (since the particle moves in a circle, it periodically passes narrow sections of the trajectory, in which its speed is directed at the observer). In addition, the power and frequency of synchrotron radiation rapidly grow with the increase of the magnetic field and particle speed. For example, fourth-generation synchrotrons emit X-ray radiation (wavelength from 0.001 to 10 nanometers), the brightness of which is hundreds of trillions of times greater than the brightness X-ray tube.
Due to these properties, with the help of synchrotron radiation it is very convenient to investigate the structure of the substance on the scales of several nanometers. In particular, using synchrotron radiation sources, scientists restore the structure of complex molecules (e.g. proteins and nucleic acids) and monitor real-time chemical reactions (e.g. battery discharge). All practical applications of synchrotron radiation are limited by its stability – the stability of the direction in which the beam, width and height of the beam are emitted, its intensity and wavelength. The weaker these values fluctuate, the higher the resolution of the picture, which can be obtained with the help of synchrotron.
In modern synchrotrons, the main source of error is fluctuations in the height of the beam, associated with the imperfection of undulators and wigglers. The noise these oscillations make to the final data is several per cent of the signal’s intensity and ten times the noise from the vibrations of everyone else values combined. Since the average measurement time at the source of synchrotron radiation rarely exceeds one millisecond, this noise cannot be removed by averaging a large number of repetitive measurements. Therefore, scientists are trying to predict possible changes in the height of the beam and correct them, adjusting the orbit of charged particles and optics through which the radiation passes.
Such adjustments often combine direct and feedback mechanisms, both of which suffer from their shortcomings. On the one hand, direct communication relies on a physical model that predicts the field of a given setting. Because the field of each component of the installation is calculated separately, this method is very demanding to the computing power of the computer. Therefore, this method is impossible to capture the rapid but relatively weak fluctuations associated with temperature fluctuations, earth tremors and tidal effects. On the other hand, feedback mechanisms take into account such small changes, but usually only work in a narrow range of parameters that only partially intersects with the real Range.
A team of physicists led by Simon Leemann has developed an algorithm based on neural networks that quickly calculates the magnetic field of the installation with relative 0.5 per cent. Using this algorithm, the scientists adjusted the magnetic field of THE ALS (Advanced Light Source). As a result, scientists were able to reduce the amplitude of vibrations of the height of the beam by an order of magnitude.
The algorithm developed was based on a neural network with a straightened (rectified) linear activation function and three hidden layers containing 128, 64 and 32 neurons, respectively. Neuroscientist scientists trained on an array containing data on both the magnetic field, the vibrations of which change the trajectory of charged particles and indirectly affect the width of the beam, and about the width of the beam itself. On the ALS synchrotron, this data can be collected at a frequency of about 10 times per second. Physics used a method to reverse the spread of the error. As a result, the trained neural network predicted the height of the beam with a margin of error of about 0.4% of the full height of the beam. In addition, the algorithm managed to get the result in just a few milliseconds, although it was launched on a normal home computer. This time is hundreds of times, during which scientists collect information from a real accelerator, so with the algorithm developed, it is possible to adjust on the fly synchrotron’s work.
Therefore, the researchers refined the algorithm and forced it to calculate how to adjust the parameters of the installation, so that fluctuations in the height of the beam were minimal. The scientists then connected the algorithm to the real ALS synchrotron. As a result, physicists were able to reduce the amplitude of beam vibrations to the error of predictions of the neural network, that is, to 0.4% of the full height of the beam (in terms of real data it’s about 0.2 micrometres). This is almost an order of magnitude higher than the amplitude of beam vibrations, adjusted with traditional algorithms (about 1.5 micrometers).
Given the success of the algorithm developed, in the future scientists plan to completely transfer the ALS synchrotron to adjustment with the help of the neural network. Physicists estimate that for a computer that is currently adjusting the installation settings, this will free up about a hundred hours of machine time per year.
Now machine learning has penetrated into almost all areas of science, and this method of solving problems has also not bypassed physics. Over the past few years, with the help of machine learning, scientists have learned to correct the mistakes of quantum computers, solve the quantum problem of many bodies, calculate the chemical properties of molecules, search for the decays of the Higgs boson, highlight the relevant degrees of freedom of physical systems, evaluate the stability of crystals, predict crystal growth and search for high-temperature ferromagnets. Most likely, in the near future, the list of physical problems solved with the help of machine learning will expand even more.