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arXiv · 2201.12468

Symbolic-Numeric Integration of Univariate Expressions based on Sparse Regression

Shahriar Iravanian·Carl Julius Martensen·Alessandro Cheli·Shashi Gowda·Anand Jain·Yingbo Ma·Chris Rackauckas
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Abstract

Most computer algebra systems (CAS) support symbolic integration as core functionality. The majority of the integration packages use a combination of heuristic algebraic and rule-based (integration table) methods. In this paper, we present a hybrid (symbolic-numeric) methodology to calculate the indefinite integrals of univariate expressions. The primary motivation for this work is to add symbolic integration functionality to a modern CAS (the symbolic manipulation packages of SciML, the Scientific Machine Learning ecosystem of the Julia programming language), which is mainly designed toward numerical and machine learning applications and has a different set of features than traditional CAS. The symbolic part of our method is based on the combination of candidate terms generation (borrowed from the Homotopy operators theory) with rule-based expression transformations provided by the underlying CAS. The numeric part is based on sparse-regression, a component of Sparse Identification of Nonlinear Dynamics (SINDy) technique. We show that this system can solve a large variety of common integration problems using only a few dozen basic integration rules.

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Shahriar Iravanian, Carl Julius Martensen, Alessandro Cheli, Shashi Gowda, Anand Jain, Yingbo Ma, Chris Rackauckas. 2022-01-29. Symbolic-Numeric Integration of Univariate Expressions based on Sparse Regression. https://arxiv.org/abs/2201.12468

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