Symbolic Integration Algorithm Selection with Machine Learning: LSTMs vs Tree LSTMs

Rashid Barket; Matthew England; Juergen Gerhard

doi:10.1007/978-3-031-64529-7_18

Symbolic Integration Algorithm Selection with Machine Learning: LSTMs vs Tree LSTMs

Rashid Barket, Matthew England, Juergen Gerhard

Research Centre for Computational Science and Mathematical Modelling

Maplesoft

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding › peer-review

1 Citation (Scopus)

29 Downloads (Pure)

Abstract

Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the output integral, and the runtime. Choosing the right sub-algorithm for a given problem is challenging: we hypothesise that Machine Learning can guide this sub-algorithm choice. A key consideration of our methodology is how to represent the mathematics to the ML model: we hypothesise that a representation which encodes the tree structure of mathematical expressions would be well suited. We trained both an LSTM and a TreeLSTM model for sub-algorithm prediction and compared them to Maple's existing approach. Our TreeLSTM performs much better than the LSTM, highlighting the benefit of using an informed representation of mathematical expressions. It is able to produce better outputs than Maple's current state-of-the-art meta-algorithm, giving a strong basis for further research.

Original language	English
Title of host publication	Mathematical Software – ICMS 2024
Subtitle of host publication	8th International Conference, Durham, UK, July 22–25, 2024, Proceedings
Editors	Kevin Buzzard, Alicia Dickenstein, Bettina Eick, Anton Leykin, Yue Ren
Publisher	Springer
Pages	167-175
Number of pages	9
Volume	14749
ISBN (Electronic)	978-3-031-64529-7
ISBN (Print)	978-3-031-64528-0
DOIs	https://doi.org/10.1007/978-3-031-64529-7_18
Publication status	Published - 2024

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Bibliographical note

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-031-64529-7_18

Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

This document is the author’s post-print version, incorporating any revisions agreed during the peer-review process. Some differences between the published version and this version may remain and you are advised to consult the published version if you wish to cite from it.

Funding

Funders	Funder number
Engineering and Physical Sciences Research Council	EP/T015748/1

Keywords

Computer Algebra
Symbolic Integration
Machine Learning
LSTM
TreeLSTM
Data Generation

Access to Document

10.1007/978-3-031-64529-7_18

England2024AAMAccepted author manuscript, 1.19 MB

Cite this

Barket, R., England, M., & Gerhard, J. (2024). Symbolic Integration Algorithm Selection with Machine Learning: LSTMs vs Tree LSTMs. In K. Buzzard, A. Dickenstein, B. Eick, A. Leykin, & Y. Ren (Eds.), Mathematical Software – ICMS 2024: 8th International Conference, Durham, UK, July 22–25, 2024, Proceedings (Vol. 14749, pp. 167-175). (Lecture Notes in Computer Science). Springer . https://doi.org/10.1007/978-3-031-64529-7_18

Symbolic Integration Algorithm Selection with Machine Learning: LSTMs vs Tree LSTMs. / Barket, Rashid ; England, Matthew; Gerhard, Juergen.
Mathematical Software – ICMS 2024: 8th International Conference, Durham, UK, July 22–25, 2024, Proceedings. ed. / Kevin Buzzard; Alicia Dickenstein; Bettina Eick; Anton Leykin; Yue Ren. Vol. 14749 Springer , 2024. p. 167-175 (Lecture Notes in Computer Science).

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding › peer-review

Barket, R , England, M & Gerhard, J 2024, Symbolic Integration Algorithm Selection with Machine Learning: LSTMs vs Tree LSTMs. in K Buzzard, A Dickenstein, B Eick, A Leykin & Y Ren (eds), Mathematical Software – ICMS 2024: 8th International Conference, Durham, UK, July 22–25, 2024, Proceedings. vol. 14749, Lecture Notes in Computer Science, Springer , pp. 167-175. https://doi.org/10.1007/978-3-031-64529-7_18

Barket R , England M, Gerhard J. Symbolic Integration Algorithm Selection with Machine Learning: LSTMs vs Tree LSTMs. In Buzzard K, Dickenstein A, Eick B, Leykin A, Ren Y, editors, Mathematical Software – ICMS 2024: 8th International Conference, Durham, UK, July 22–25, 2024, Proceedings. Vol. 14749. Springer . 2024. p. 167-175. (Lecture Notes in Computer Science). Epub 2024 Jul 17. doi: 10.1007/978-3-031-64529-7_18

Barket, Rashid ; England, Matthew ; Gerhard, Juergen. / Symbolic Integration Algorithm Selection with Machine Learning : LSTMs vs Tree LSTMs. Mathematical Software – ICMS 2024: 8th International Conference, Durham, UK, July 22–25, 2024, Proceedings. editor / Kevin Buzzard ; Alicia Dickenstein ; Bettina Eick ; Anton Leykin ; Yue Ren. Vol. 14749 Springer , 2024. pp. 167-175 (Lecture Notes in Computer Science).

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Symbolic Integration Algorithm Selection with Machine Learning: LSTMs vs Tree LSTMs

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