Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

Condensed Matter Theories

The distribution of electric charge in atomic nuclei is fundamental to our understanding of the complex nuclear dynamics and a quintessential observable to validate nuclear structure models. The aim of this study is to explore a novel approach that combines sophisticated models of nuclear structure with Bayesian neural networks (BNN) to generate predictions for the charge radii of thousands of nuclei throughout the nuclear chart. A class of relativistic energy density functionals is used to provide robust predictions for nuclear charge radii. In turn, these predictions are refined through Bayesian learning for a neural network that is trained using residuals between theoretical predictions and the experimental data. Although predictions obtained with density functional theory provide a fairly good description of experiment, our results show significant improvement (better than 40%) after BNN refinement. Moreover, these improved results for nuclear charge radii are supplemented with theoretical error bars. We have successfully demonstrated the ability of the BNN approach to significantly increase the accuracy of nuclear models in the predictions of nuclear charge radii. However, as many before us, we failed to uncover the underlying physics behind the intriguing behavior of charge radii along the calcium isotopic chain.

https://iopscience.iop.org/article/10.1088/0954-3899/43/11/114002/pdf

Nuclear charge radii: density functional theory meets Bayesian neural networks

A study on ground-state energies of nuclei by using neural networks

Resorting to a neural network approach we refined several representative and sophisticated global nuclear mass models within the latest atomic mass evaluation (AME2012). In the training process, a quite robust algorithm named the Levenberg–Marquardt (LM) method is employed to determine the weights and biases of the neural network. As a result, this LM neural network approach demonstrates a very useful tool for further improving the accuracy of mass models. For a simple liquid drop formula the root mean square (rms) deviation between the predictions and the 2353 experimental known masses are sharply reduced from 2.455 MeV to 0.235 MeV, and for the other revisited mass models, the rms is remarkably improved by about 30%.

https://iopscience.iop.org/article/10.1088/1361-6471/aa5d78/pdf

Performance of the Levenberg-Marquardt neural network approach in nuclear mass prediction

Advances in statistical learning theory present the opportunity to develop statistical models of quantum many-body systems exhibiting remarkable predictive power. The potential of such "theory-thin" approaches is illustrated with the application of Support Vector Machines (SVMs) to global prediction of nuclear properties as functions of proton and neutron numbers Z and N across the nuclidic chart. Based on the principle of structural-risk minimization, SVMs learn from examples in the existing database of a given property Y, automatically and optimally identify a set of "support vectors" corresponding to representative nuclei in the training set, and approximate the mapping (Z, N) → Y in terms of these nuclei. Results are reported for nuclear masses, beta-decay lifetimes, and spins/parities of nuclear ground states. These results indicate that SVM models can match or even surpass the predictive performance of the best conventional "theory-thick" global models based on nuclear phenomenology.

Application of support vector machines to global prediction of nuclear properties

Reliable estimates of halflives for β−-decaying nuclei far from the stability line are needed for the experimental exploration of the nuclear landscape at radioactive beam facilities and for studies of nuclear astrophysical processes, notably r-process nucleosynthesis [1]. A constellation of theory-thick, macroscopic or semi-microscopic models has been developed during the last decades for generating β−-decay halflives. However, the predictive power of these models is rather limited for nuclides far from stability (and often inaccessible to experiment). The recent advances in statistical learning theory present, on the other hand, the opportunity to develop statistical models of quantum many-body systems exhibiting remarkable predictive power. Statistical modeling of nuclear data, using Artificial Neural Networks (ANNs) [2, 3, 4] and more recently Support Vector Machines (SVMs) [5, 6], is providing a complementary theory-thin approach to the prediction of nuclear systematics. In this work, we examine the potential of such theory-thin approaches via a detailed comparison of halflife estimates of neutron-rich β− unstable nuclei produced by the global models developed using ANNs and SVMs. The former have been developed by following the methodology of reference [4] for each class of nuclei with given even-odd character in Z, N that decay 100% by the β− mode in their ground states. Corresponding models using the same data sets have been developed by means of SVMs in reference [6]. The halflife estimates generated by both types of machines are discussed and compared with the available experimental data [7], with previous results obtained with neural networks [8], and with estimates coming from traditional global nuclear models. Particular attention is paid to r-process nuclides. Our results demonstrate that in the framework of the β−-decay problem considered here the statistical models based on machine learning can match or even surpass the predictive performance of the best conventional theory-thick global models based on nuclear phenomenology. Regarding extrapability, the models based on Multilayer Feedforward Neural Networks are slightly better than those based on SVMs. Accordingly, work is in progress to develop global statistical models of other quantities of nuclear systematics using both techniques of machine learning.

/pdf/statistical-global-modeling-of-b-decay-halflives-systematics-25kcoz9a6k.pdf

Statistical Global Modeling of β−-Decay Halflives Systematics Using Multilayer Feedforward Neural Networks and Support Vector Machines

Advances in statistical learning theory present the opportunity to develop statistical models of quantum many-body systems exhibiting remarkable predictive power. The potential of such ``theory-thin'' approaches is illustrated with the application of Support Vector Machines (SVMs) to global prediction of nuclear properties as functions of proton and neutron numbers $Z$ and $N$ across the nuclidic chart. Based on the principle of structural-risk minimization, SVMs learn from examples in the existing database of a given property $Y$, automatically and optimally identify a set of ``support vectors'' corresponding to representative nuclei in the training set, and approximate the mapping $(Z,N) \to Y$ in terms of these nuclei. Results are reported for nuclear masses, beta-decay lifetimes, and spins/parities of nuclear ground states. These results indicate that SVM models can match or even surpass the predictive performance of the best conventional ``theory-thick'' global models based on nuclear phenomenology.

https://arxiv.org/pdf/nucl-th/0603037.pdf

Application Of Support Vector Machines To Global Prediction Of Nuclear Properties

In this work, the beta-decay halflives problem is dealt as a nonlinear optimization problem, which is resolved in the statistical framework of Machine Learning (LM). Continuing past similar approaches, we have constructed sophisticated Artificial Neural Networks (ANNs) and Support Vector Regression Machines (SVMs) for each class with even-odd character in Z and N to global model the systematics of nuclei that decay 100% by the beta-minus-mode in their ground states. The arising large-scale lifetime calculations generated by both types of machines are discussed and compared with each other, with the available experimental data, with previous results obtained with neural networks, as well as with estimates coming from traditional global nuclear models. Particular attention is paid on the estimates for exotic and halo nuclei and we focus to those nuclides that are involved in the r-process nucleosynthesis. It is found that statistical models based on LM can at least match or even surpass the predictive performance of the best conventional models of beta-decay systematics and can complement the latter.

Statistical Global Modeling of Beta-Decay Halflives Systematics Using Multilayer Feedforward Neural Networks and Support Vector Machines

Properties of the distribution of single-particle levels adjacent to the Fermi surface in finite Fermi systems are studied, focusing on the case in which these levels are degenerate The interaction of the quasiparticles occupying these levels lifts the degeneracy and affects the distance between the closest levels on opposite sides of the Fermi surface, as the number of particles in the system is varied In addition to the familiar scenario of level crossing, a new phenomenon is uncovered, in which the merging of single-particle levels results in the disappearance of well-defined single-particle excitations Implications of this finding are discussed for nuclear, solid-state, and atomic systems

Haochen Li

Papers

Application of support vector machines to global prediction of nuclear properties

Statistical Global Modeling of β−-Decay Halflives Systematics Using Multilayer Feedforward Neural Networks and Support Vector Machines

Application Of Support Vector Machines To Global Prediction Of Nuclear Properties

Statistical Global Modeling of Beta-Decay Halflives Systematics Using Multilayer Feedforward Neural Networks and Support Vector Machines

Merging of single-particle levels in finite Fermi systems