arXiv subjects

Katia Matcheva

Publications and source records attributed to Katia Matcheva.

30 records · Page 2Linked to original sources

arXiv2023

Reproducing Bayesian Posterior Distributions for Exoplanet Atmospheric Parameter Retrievals with a Machine Learning Surrogate Model

We describe a machine-learning-based surrogate model for reproducing the Bayesian posterior distributions for exoplanet atmospheric parameters derived from transmission spectra of transiting planets with typical retrieval software such as TauRex. The model is trained on ground truth distributions for seven parameters: the planet radius, the atmospheric temperature, and the mixing ratios for five common absorbers: $H_2O$, $CH_4$, $NH_3$, $CO$ and $CO_2$. The model performance is enhanced by domain-inspired preprocessing of the features and the use of semi-supervised learning in order to leverage the large amount of unlabelled training data available. The model was among the winning solutions in the 2023 Ariel Machine Learning Data Challenge.

astro-ph.EP↗

arXiv2023

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.

hep-ph↗

arXiv2023

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.

astro-ph.EP↗

arXiv2023

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 $G_2$, $F_4$, and $E_6$. 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.

hep-th↗

arXiv2023

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 $U(n)$ and $SU(n)$ families of Lie groups. This approach is completely general and can be used to find the infinitesimal generators for any Lie group.

hep-ph↗

arXiv2023

Oracle-Preserving Latent Flows

We develop a deep learning methodology for the simultaneous discovery of multiple nontrivial continuous symmetries across an entire labelled dataset. The symmetry transformations and the corresponding generators are modeled with fully connected neural networks trained with a specially constructed loss function ensuring the desired symmetry properties. The two new elements in this work are the use of a reduced-dimensionality latent space and the generalization to transformations invariant with respect to high-dimensional oracles. The method is demonstrated with several examples on the MNIST digit dataset.

cs.LG↗

arXiv2023

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. We construct loss functions that ensure that the applied transformations are symmetries and that 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 $SO(1,3)$. 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.

hep-ph↗

arXiv2022

Is the Machine Smarter than the Theorist: Deriving Formulas for Particle Kinematics with Symbolic Regression

We demonstrate the use of symbolic regression in deriving analytical formulas, which are needed at various stages of a typical experimental analysis in collider phenomenology. As a first application, we consider kinematic variables like the stransverse mass, $M_{T2}$, which are defined algorithmically through an optimization procedure and not in terms of an analytical formula. We then train a symbolic regression and obtain the correct analytical expressions for all known special cases of $M_{T2}$ in the literature. As a second application, we reproduce the correct analytical expression for a next-to-leading order (NLO) kinematic distribution from data, which is simulated with a NLO event generator. Finally, we derive analytical approximations for the NLO kinematic distributions after detector simulation, for which no known analytical formulas currently exist.

hep-ph↗

arXiv2022

Transverse Vector Decomposition Method for Analytical Inversion of Exoplanet Transit Spectra

We develop a new method for analytical inversion of binned exoplanet transit spectra and for retrieval of planet parameters. The method has a geometrical interpretation and treats each observed spectrum as a single vector $\vec r$ in the multidimensional spectral space of observed bin values. We decompose the observed $\vec{r}$ into a wavelength-independent component $\vec{r}_\parallel$ corresponding to the spectral mean across all observed bins, and a transverse component $\vec{r}_\perp$ which is wavelength-dependent and contains the relevant information about the atmospheric chemistry. The method allows us to extract, without any prior assumptions or additional information, the relative mass (or volume) mixing ratios of the absorbers in the atmosphere, the scale height to stellar radius ratio, $H/R_S$, and the atmospheric temperature. The method is illustrated and validated with several examples of increasing complexity.

astro-ph.EP↗

arXiv2022

Unsupervised Machine Learning for Exploratory Data Analysis of Exoplanet Transmission Spectra

Transit spectroscopy is a powerful tool to decode the chemical composition of the atmospheres of extrasolar planets. In this paper we focus on unsupervised techniques for analyzing spectral data from transiting exoplanets. We demonstrate methods for i) cleaning and validating the data, ii) initial exploratory data analysis based on summary statistics (estimates of location and variability), iii) exploring and quantifying the existing correlations in the data, iv) pre-processing and linearly transforming the data to its principal components, v) dimensionality reduction and manifold learning, vi) clustering and anomaly detection, vii) visualization and interpretation of the data. To illustrate the proposed unsupervised methodology, we use a well-known public benchmark data set of synthetic transit spectra. We show that there is a high degree of correlation in the spectral data, which calls for appropriate low-dimensional representations. We explore a number of different techniques for such dimensionality reduction and identify several suitable options in terms of summary statistics, principal components, etc. We uncover interesting structures in the principal component basis, namely, well-defined branches corresponding to different chemical regimes of the underlying atmospheres. We demonstrate that those branches can be successfully recovered with a K-means clustering algorithm in fully unsupervised fashion. We advocate for a three-dimensional representation of the spectroscopic data in terms of the first three principal components, in order to reveal the existing structure in the data and quickly characterize the chemical class of a planet.

astro-ph.EP↗

arXiv2021

Analytical Modelling of Exoplanet Transit Specroscopy with Dimensional Analysis and Symbolic Regression

The physical characteristics and atmospheric chemical composition of newly discovered exoplanets are often inferred from their transit spectra which are obtained from complex numerical models of radiative transfer. Alternatively, simple analytical expressions provide insightful physical intuition into the relevant atmospheric processes. The deep learning revolution has opened the door for deriving such analytical results directly with a computer algorithm fitting to the data. As a proof of concept, we successfully demonstrate the use of symbolic regression on synthetic data for the transit radii of generic hot Jupiter exoplanets to derive a corresponding analytical formula. As a preprocessing step, we use dimensional analysis to identify the relevant dimensionless combinations of variables and reduce the number of independent inputs, which improves the performance of the symbolic regression. The dimensional analysis also allowed us to mathematically derive and properly parametrize the most general family of degeneracies among the input atmospheric parameters which affect the characterization of an exoplanet atmosphere through transit spectroscopy.

astro-ph.EP↗

arXiv2010

The 1998 November 14 Occultation of GSC 0622-00345 by Saturn. II. Stratospheric Thermal Profile, Power Spectrum, and Gravity Waves

On 1998 November 14, Saturn and its rings occulted the star GSC 0622-00345. The occultation latitude was 55.5 degrees S. This paper analyzes the 2.3 μm light curve derived by Harrington & French. A fixed-baseline isothermal fit to the light curve has a temperature of 140 +/- 3 K, assuming a mean molecular mass of 2.35 AMU. The thermal profile obtained by numerical inversion is valid between 1 and 60 μbar. The vertical temperature gradient is >0.2 K/km more stable than the adiabatic lapse rate, but it still shows the alternating-rounded-spiked features seen in many temperature gradient profiles from other atmospheric occultations and usually attributed to breaking gravity (buoyancy) waves. We conduct a wavelet analysis of the thermal profile, and show that, even with our low level of noise, scintillation due to turbulence in Earth's atmosphere can produce large temperature swings in light-curve inversions. Spurious periodic features in the "reliable" region of a wavelet amplitude spectrum can exceed 0.3 K in our data. We also show that gravity-wave model fits to noisy isothermal light curves can lead to convincing wave "detections". We provide new significance tests for localized wavelet amplitudes, wave model fits, and global power spectra of inverted occultation light curves by assessing the effects of pre- and post-occultation noise on these parameters. Based on these tests, we detect several significant ridges and isolated peaks in wavelet amplitude, to which we fit a gravity wave model. We also strongly detect the global power spectrum of thermal fluctuations in Saturn's atmosphere, which resembles the "universal" (modified Desaubies) curve associated with saturated spectra of propagating gravity waves on Earth and Jupiter.

astro-ph.EP↗