30 April 2024
Functional equations appear in many scientific areas of study due to their ability to efficiently model complex phenomena. Unfortunately, when analytical solutions are not available, finding approximate solutions using numerical methods such as semidefinite programming can often be computationally expensive. Although numerical methods can be quite effective, often they only provide bounds on the parameters of the equation. Differential Equations (DEs) and Partial Differential Equations (PDEs) can also be interpreted as functional equations and have been widely studied with both numerical and Machine Learning methods.
In this work, EMERGE partners from the University of Pisa develop MultiSTOP, a Reinforcement Learning framework for solving functional equations in physics. This new methodology is also able to find actual numerical solutions instead of bounds. The authors extend the original BootSTOP algorithm by adding multiple constraints derived from domain-specific knowledge, even in integral form, to improve the accuracy of the solution.
Read the paper in the link below.
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