Tag Archives: Symbolic Computation

Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl [IMA]

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http://arxiv.org/abs/2305.01582


PySR is an open-source library for practical symbolic regression, a type of machine learning which aims to discover human-interpretable symbolic models. PySR was developed to democratize and popularize symbolic regression for the sciences, and is built on a high-performance distributed back-end, a flexible search algorithm, and interfaces with several deep learning packages. PySR’s internal search algorithm is a multi-population evolutionary algorithm, which consists of a unique evolve-simplify-optimize loop, designed for optimization of unknown scalar constants in newly-discovered empirical expressions. PySR’s backend is the extremely optimized Julia library SymbolicRegression.jl, which can be used directly from Julia. It is capable of fusing user-defined operators into SIMD kernels at runtime, performing automatic differentiation, and distributing populations of expressions to thousands of cores across a cluster. In describing this software, we also introduce a new benchmark, “EmpiricalBench,” to quantify the applicability of symbolic regression algorithms in science. This benchmark measures recovery of historical empirical equations from original and synthetic datasets.

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M. Cranmer
Wed, 3 May 23
23/67

Comments: 24 pages, 5 figures, 3 tables. Feedback welcome. Paper source found at this https URL ; PySR at this https URL ; SymbolicRegression.jl at this https URL

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

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http://arxiv.org/abs/2112.11600


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.

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K. Matchev, K. Matcheva and A. Roman
Thu, 23 Dec 21
36/63

Comments: Submitted to AAS Journals, 24 pages, 7 figures

NRPyLaTeX: A LaTeX interface to computer algebra systems for general relativity [CL]

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http://arxiv.org/abs/2111.05861


While each computer algebra system (CAS) contains its own unique syntax for inputting mathematical expressions, LaTeX is perhaps the most widespread language for typesetting mathematics. NRPyLaTeX (NL) enables direct LaTeX input of complex tensorial expressions (written in Einstein notation) relevant to general relativity and differential geometry into the SymPy CAS. As SymPy also supports output compatible with the Mathematica and Maple CASs, NL lowers the learning curve for inputting and manipulating tensorial expressions in three widely used CASs. LaTeX however is a typesetting language, and as such is not designed to resolve ambiguities in mathematical expressions. To address this, NL implements a convenient configuration interface that, e.g., defines variables/keywords and assigns properties/attributes to them. Configuration commands appear as LaTeX comments, so that entire NL workflows can fit seamlessly into the LaTeX source code of scientific papers without interfering with the rendered mathematical expressions. Further, NL adopts NRPy+’s rigid syntax for indexed symbols (e.g., tensors), which enables NL output to be directly converted into highly optimized C/C++-code kernels using NRPy+. Finally NL has robust and user-friendly error-handling, which catches common tensor indexing errors and reports unresolved ambiguities, further expediting the input and validation of LaTeX expressions into a CAS.

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K. Sible and Z. Etienne
Fri, 12 Nov 21
15/53

Comments: 16 pages, 10 figures

$\mathtt{bimEX}$: A Mathematica package for exact computations in 3$+$1 bimetric relativity [CL]

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http://arxiv.org/abs/1904.10464


We present $\mathtt{bimEX}$, a Mathematica package for exact computations in 3$+$1 bimetric relativity. It is based on the $\mathtt{xAct}$ bundle, which can handle computations involving both abstract tensors and their components. In this communication, we refer to the latter case as concrete computations. The package consists of two main parts. The first part involves the abstract tensors, and focuses on how to deal with multiple metrics in $\mathtt{xAct}$. The second part takes an ansatz for the primary variables in a chart as the input, and returns the covariant BSSN bimetric equations in components in that chart. Several functions are implemented to make this process as fast and user-friendly as possible. The package has been used and tested extensively in spherical symmetry and was the workhorse in obtaining the bimetric covariant BSSN equations and reproducing the bimetric 3$+$1 equations in the spherical polar chart.

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F. Torsello
Thu, 25 Apr 19
5/58

Comments: 9 pages. The ancillary files contain the main paper with bibliographic tooltips. GitHub repository at this https URL