10 research outputs found
Searching for Novel Chemistry in Exoplanetary Atmospheres using Machine Learning for Anomaly Detection
The next generation of telescopes will yield a substantial increase in the
availability of high-resolution spectroscopic data for thousands of exoplanets.
The sheer volume of data and number of planets to be analyzed greatly motivate
the development of new, fast and efficient methods for flagging interesting
planets for reobservation and detailed analysis. We advocate the application of
machine learning (ML) techniques for anomaly (novelty) detection to exoplanet
transit spectra, with the goal of identifying planets with unusual chemical
composition and even searching for unknown biosignatures. We successfully
demonstrate the feasibility of two popular anomaly detection methods (Local
Outlier Factor and One Class Support Vector Machine) on a large public database
of synthetic spectra. We consider several test cases, each with different
levels of instrumental noise. In each case, we use ROC curves to quantify and
compare the performance of the two ML techniques.Comment: Submitted to AAS Journals, 30 pages, 14 figure
Discovering Sparse Representations of Lie Groups with Machine Learning
Recent work has used deep learning to derive symmetry transformations, which
preserve conserved quantities, and to obtain the corresponding algebras of
generators. In this letter, we extend this technique to derive sparse
representations of arbitrary Lie algebras. We show that our method reproduces
the canonical (sparse) representations of the generators of the Lorentz group,
as well as the and families of Lie groups. This approach is
completely general and can be used to find the infinitesimal generators for any
Lie group.Comment: 14 pages, 6 figure
Identifying the Group-Theoretic Structure of Machine-Learned Symmetries
Deep learning was recently successfully used in deriving symmetry
transformations that preserve important physics quantities. Being completely
agnostic, these techniques postpone the identification of the discovered
symmetries to a later stage. In this letter we propose methods for examining
and identifying the group-theoretic structure of such machine-learned
symmetries. We design loss functions which probe the subalgebra structure
either during the deep learning stage of symmetry discovery or in a subsequent
post-processing stage. We illustrate the new methods with examples from the
U(n) Lie group family, obtaining the respective subalgebra decompositions. As
an application to particle physics, we demonstrate the identification of the
residual symmetries after the spontaneous breaking of non-Abelian gauge
symmetries like SU(3) and SU(5) which are commonly used in model building.Comment: 10 pages, 8 figures, 2 table
Searching for Novel Chemistry in Exoplanetary Atmospheres Using Machine Learning for Anomaly Detection
The next generation of telescopes will yield a substantial increase in the availability of high-quality spectroscopic data for thousands of exoplanets. The sheer volume of data and number of planets to be analyzed greatly motivate the development of new, fast, and efficient methods for flagging interesting planets for reobservation and detailed analysis. We advocate the application of machine learning (ML) techniques for anomaly (novelty) detection to exoplanet transit spectra, with the goal of identifying planets with unusual chemical composition and even searching for unknown biosignatures. We successfully demonstrate the feasibility of two popular anomaly detection methods (local outlier factor and one-class support vector machine) on a large public database of synthetic spectra. We consider several test cases, each with different levels of instrumental noise. In each case, we use receiver operating characteristic curves to quantify and compare the performance of the two ML techniques
Identifying the group-theoretic structure of machine-learned symmetries
Deep learning was recently successfully used in deriving symmetry transformations that preserve important physics quantities. Being completely agnostic, these techniques postpone the identification of the discovered symmetries to a later stage. In this letter we propose methods for examining and identifying the group-theoretic structure of such machine-learned symmetries. We design loss functions which probe the subalgebra structure either during the deep learning stage of symmetry discovery or in a subsequent post-processing stage. We illustrate the new methods with examples from the U(n) Lie group family, obtaining the respective subalgebra decompositions. As an application to particle physics, we demonstrate the identification of the residual symmetries after the spontaneous breaking of non-Abelian gauge symmetries like SU(3) and SU(5) which are commonly used in model building
Accelerated Discovery of Machine-Learned Symmetries: Deriving the Exceptional Lie Groups G2, F4 and E6
Recent work has applied supervised deep learning to derive continuous
symmetry transformations that preserve the data labels and to obtain the
corresponding algebras of symmetry generators. This letter introduces two
improved algorithms that significantly speed up the discovery of these symmetry
transformations. The new methods are demonstrated by deriving the complete set
of generators for the unitary groups U(n) and the exceptional Lie groups ,
, and . A third post-processing algorithm renders the found
generators in sparse form. We benchmark the performance improvement of the new
algorithms relative to the standard approach. Given the significant complexity
of the exceptional Lie groups, our results demonstrate that this
machine-learning method for discovering symmetries is completely general and
can be applied to a wide variety of labeled datasets.Comment: 11 pages, 7 figure
Accelerated discovery of machine-learned symmetries: Deriving the exceptional Lie groups G2, F4 and E6
Recent work has applied supervised deep learning to derive continuous symmetry transformations that preserve the data labels and to obtain the corresponding algebras of symmetry generators. This letter introduces two improved algorithms that significantly speed up the discovery of these symmetry transformations. The new methods are demonstrated by deriving the complete set of generators for the unitary groups U(n) and the exceptional Lie groups G2, F4, and E6. A third post-processing algorithm renders the found generators in sparse form. We benchmark the performance improvement of the new algorithms relative to the standard approach. Given the significant complexity of the exceptional Lie groups, our results demonstrate that this machine-learning method for discovering symmetries is completely general and can be applied to a wide variety of labeled datasets
Deep learning symmetries and their Lie groups, algebras, and subalgebras from first principles
We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the symmetry transformations and the corresponding generators. The constructed loss functions ensure that the applied transformations are symmetries and the corresponding set of generators forms a closed (sub)algebra. Our procedure is validated with several examples illustrating different types of conserved quantities preserved by symmetry. In the process of deriving the full set of symmetries, we analyze the complete subgroup structure of the rotation groups SO (2), SO (3), and SO (4), and of the Lorentz group . Other examples include squeeze mapping, piecewise discontinuous labels, and SO (10), demonstrating that our method is completely general, with many possible applications in physics and data science. Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties
Emergence of distinct electronic states in epitaxially-fused PbSe quantum dot superlattices
Quantum coupling in arrayed nanostructures can produce novel mesoscale properties such as electronic minibands to improve the performance of optoelectronic devices, including ultra-efficient solar cells and infrared photodetectors. Colloidal PbSe quantum dots (QDs) that self-assemble into epitaxially-fused superlattices (epi-SLs) are predicted to exhibit such collective phenomena. Here, we show the emergence of distinct local electronic states induced by crystalline necks that connect individual PbSe QDs and modulate the bandgap energy across the epi-SL. Multi-probe scanning tunneling spectroscopy shows bandgap modulation from 0.7 eV in the QDs to 1.1 eV at their necks. Complementary monochromated electron energy-loss spectroscopy demonstrates bandgap modulation in spectral mapping, confirming the presence of these distinct energy states from necking. The results show the modification of the electronic structure of a precision-made nanoscale superlattice, which may be leveraged in new optoelectronic applications