Development of Highly Accurate Integration AI Using Deep Learning: Highest Score Ever Achieved by AI in Symbolic Integration Tests
May 27, 2022 Keio University
A research group comprising Hazumi Kubota and Yuta Tokuoka (of the same affiliation at time of study) of the Keio University Graduate School of Science and Technology, and Assistant Professor Takahiro Yamada, and Professor Akira Funahashi of the Faculty of Science and Technology have developed AIs capable of predicting the integrated function (primitive function) from the input function subject to integration (integrand), after remarking on the similarities between the mathematical processing of integrals learned in high school and those for language translation using AIs, which have seen remarkable progress in recent years. Taking inspiration from the fact that it is possible to determine the accuracy of integration from taking a differentiated primitive function produced by AI and determining whether it is consistent with the integrand, the group developed a method for creating and training diverse AIs, and deploying those AIs capable of producing the correct answer from among these. These results demonstrate that the developed AIs were capable of integration to an accuracy of 99.79%, the highest ratio ever achieved when compared to previously developed integration tools such as Mathematica and other machine learning methods. Furthermore, investigating the characteristics of the functions learned by the AI revealed that each of the constructed models had functions to which they were suited and those to which they were less suited when performing integrations. Accordingly, these models were capable of facilitating high degrees of accuracy by solving integrations in a cross-subsidized manner. Integration is an essential process for simulations in control engineering, systems biology, and other domains, and these results are anticipated to contribute to increasingly accurate simulations in these fields.
Prior to their publication in the journal IEEE Access, a preliminary online version of these research results was published on the journal's website on April 29.
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