Using machine learning to make a computer learn calculus

Question

Are there any known approaches of making a machine learn calculus?

I've learnt that it is quite simple to teach calculating derivatives because it is possible to implement an algorithm.

Meanwhile, an implementation of integration is possible but is rarely or never fully implemented due to the algorithmic complexity.

I am curious whether there are any academic successes in the field of using machine learning science to evaluate and calculate integrals.

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Edit

I am interested in teaching a computer to integrate using neural networks or similar methods.

Answer 1

My personal opinion it is not possible to feed into NN enough rules for integrating. Why? Because NN are good for linear regression ( AKA approximation ) or logical regression ( AKA classification ). Integration is neither of them. It is calculation task according to some strict algorithms. So from this prospective it's good idea to use some mathematical ways to integrate.
Update on 2020-10-23
Right now I'm in position of being ashamed by new developments according to news. Facebook recently announced that they developed some kind of AI, which is good in solving integrations.

Answer 2

There quite a few number of maths software that will compute derivatives and integral calculus for you. Some of the popular software include MATLAB, Maple, Mathematica, etc. These software will help you learn quite easily.

As for you making a machine learn calculus ... You can read up on the following on wikipedia or other books,

Newton's Method - Solve the roots of a function numerically

Monte Carlo Integration - uses RNG to compute numeric integration

Runge Kutta Method - Solves ODE's iteratively

There are many more. These are just the ones I was taught in undergraduate school. They are also fairly simple to understand, depending on your level of academia. But in general, people have been try to numerically compute solutions to models since Newton. Computers have just made everything a lot easier.