Accelerating Understanding of Scientific Experiments with End to End Symbolic Regression

Aréchiga, Nikos; Chen, Francine; Chen, Yanying; Zhang, Yanxia; Iliev, Rumen; Toyoda, Heishiro; Lyons, Kent

doi:10.48550/arxiv.2112.04023

Cited by 6 publications

(10 citation statements)

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“…For concreteness, we use the recently proposed PySR framework (Cranmer et al 2020), which uses a genetic algorithm to perform symbolic regression. 2 Similar studies have been done in several physical domains (Battaglia et al 2016;Chang et al 2016;Iten et al 2020;Udrescu & Tegmark 2020;Arechiga et al 2021;Lemos et al 2022), but to the best of our knowledge, not in exoplanetary science.…”

Section: Introductionmentioning

confidence: 63%

Analytical Modeling of Exoplanet Transit Spectroscopy with Dimensional Analysis and Symbolic Regression

Matchev

Matcheva

Roman

2022

ApJ

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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 parameterize the most general family of degeneracies among the input atmospheric parameters that affect the characterization of an exoplanet atmosphere through transit spectroscopy.

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Section: Introductionmentioning

confidence: 63%

Analytical Modeling of Exoplanet Transit Spectroscopy with Dimensional Analysis and Symbolic Regression

Matchev

Matcheva

Roman

2022

ApJ

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“…More recently, ML is also being used to facilitate tasks that traditionally have fallen within the domain of theorists, e.g. performing symbolic computations [6,7] or deriving analytical formulas by training a symbolic regression on synthetic data [8][9][10][11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Deep learning symmetries and their Lie groups, algebras, and subalgebras from first principles

Forestano

Matchev

Matcheva

et al. 2023

Mach. Learn.: Sci. Technol.

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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 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.

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“…We note that while they do have the expected form for a generator of rotations in two dimensions, they are essentially the same transformation, and differ only by an overall sign. This implies that they fail the orthogonality condition -indeed, we find that the dominant contribution to the large total loss in that case is from the orthogonality loss (13). Since the total loss is large and does not improve with further training (see the orange line for N g = 2 in Figure 2), these two are not valid generators and should be discarded.…”

Section: Length-preserving Transformations In Two Dimensionsmentioning

confidence: 89%

“…Over the last decade, there has been increased interest in applications of machine learning (ML) to highdimensional physics data as a sensitive tool for event simulation, data analysis, and statistical inference [3][4][5]. More recently, ML is also being used to facilitate tasks that traditionally have fallen within the domain of theorists, e.g., performing symbolic computations [6,7] or deriving analytical formulas by training a symbolic regression on synthetic data [8][9][10][11][12][13][14][15][16][17][18][19][20].…”

mentioning

confidence: 99%

Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles

Forestano¹,

Matchev²,

Matcheva³

et al. 2023

Preprint

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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.

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Accelerating Understanding of Scientific Experiments with End to End Symbolic Regression

Cited by 6 publications

References 0 publications

Analytical Modeling of Exoplanet Transit Spectroscopy with Dimensional Analysis and Symbolic Regression

Analytical Modeling of Exoplanet Transit Spectroscopy with Dimensional Analysis and Symbolic Regression

Deep learning symmetries and their Lie groups, algebras, and subalgebras from first principles

Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles

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