On mathematica program for “Poor Man’s Integrator” implementing Risch-Norman algorithm

Kragler, R.

doi:10.1134/s0361768809020029

Cited by 2 publications

(1 citation statement)

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“…In particular, there are many differential equations and integration problems that are known to have no closed-form analytic solution, which would be guaranteed to fail in these systems (Kragler 2009).…”

Section: Strengths and Advantagesmentioning

confidence: 99%

A Neuro-Symbolic Method for Solving Differential and Functional Equations

Panju,

Ghodsi

2020

Preprint

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When neural networks are used to solve differential equations, they usually produce solutions in the form of black-box functions that are not directly mathematically interpretable. We introduce a method for generating symbolic expressions to solve differential equations while leveraging deep learning training methods. Unlike existing methods, our system does not require learning a language model over symbolic mathematics, making it scalable, compact, and easily adaptable for a variety of tasks and configurations. As part of the method, we propose a novel neural architecture for learning mathematical expressions to optimize a customizable objective. The system is designed to always return a valid symbolic formula, generating a useful approximation when an exact analytic solution to a differential equation is not or cannot be found. We demonstrate through examples how our method can be applied on a number of differential equations, often obtaining symbolic approximations that are useful or insightful. Furthermore, we show how the system can be effortlessly generalized to find symbolic solutions to other mathematical tasks, including integration and functional equations.

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Section: Strengths and Advantagesmentioning

confidence: 99%