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Deriving Compact Laws Based on Algebraic Formulation of a Data Set

Xu, Wenqing (William) and Stalzer, Mark (2019) Deriving Compact Laws Based on Algebraic Formulation of a Data Set. Journal of Computational Science, 36 . Art. No. 101009. ISSN 1877-7503. https://resolver.caltech.edu/CaltechAUTHORS:20190617-104717869

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Abstract

In various subjects, there exist concise and consistent relationships between input and output parameters. Discovering the relationships, or more precisely compact laws, in a data set is of great interest in many fields, such as physics, chemistry, and finance. In recent years, the field of data discovery has made great progress towards discovering these laws in practice thanks to the success of machine learning. However, machine learning methods relate the input and output data by considering them separately instead of equally. In addition, the analytical approaches to finding the underlying theories governing the data are relatively slow. In this paper, we develop an innovative approach on discovering compact laws. A novel algebraic equation formulation is proposed such that constant determination and candidate equation verification can be explicitly solved with low computational time. This algebraic equation formulation does not distinguish between input and output variables, and converts the problem of deriving meaning from data into solving a linear algebra equation and searching for linear equations that fit the data. We also derive a more efficient search algorithm using finite fields. Rigorous proofs and computational results are presented in validating these methods. The algebraic formulation allows for the search of equation candidates in an explicit mathematical manner. For a certain type of compact theory, our approach assures convergence, with the discovery being computationally efficient and mathematically precise.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.jocs.2019.06.006DOIArticle
https://arxiv.org/abs/1706.05123arXivDiscussion Paper
Additional Information:© 2019 Published by Elsevier. Received 23 July 2018, Revised 14 January 2019, Accepted 13 June 2019, Available online 15 June 2019. This research was funded by the Gordon and Betty Moore Foundation through Grant GBMF4915 to the Caltech Center for Data-Driven Discovery. This researched was conducted as the named Caltech SURF program of Dr. Jane Chen.
Funders:
Funding AgencyGrant Number
Gordon and Betty Moore FoundationGBMF4915
Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
Record Number:CaltechAUTHORS:20190617-104717869
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190617-104717869
Official Citation:Wenqing (William) Xu, Mark Stalzer, Deriving compact laws based on algebraic formulation of a data set, Journal of Computational Science, Volume 36, 2019, 101009, ISSN 1877-7503, https://doi.org/10.1016/j.jocs.2019.06.006. (http://www.sciencedirect.com/science/article/pii/S1877750318307609)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:96463
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:17 Jun 2019 19:51
Last Modified:03 Oct 2019 21:22

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