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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.

Edit

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

Nikaido
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Mateusz Piotrowski
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2 Answers2

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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.

Yuriy Zaletskyy
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    The data can't be a problem, you can always generate more training samples. There are attempts (google for Learning to Execute) to make modern neural networks learn algorithms from the data. – Artem Sobolev Apr 24 '15 at 13:16
  • Yes, you can generate functions, but you can't generate integrals of functions with such an ease. Especially if function is complicated. For example sin(x) * x * arctg(x)* x! + e^x * cos(x) * ln(x^(tan(x))) – Yuriy Zaletskyy Apr 24 '15 at 13:29
  • that's what I was asking :) is it possible to train a NN to recognize certain patterns people use to solve integrals – Mateusz Piotrowski Apr 24 '15 at 13:42
  • NN will not provide you exact answer, but approximate. NN are good approximators and not good in calculation tasks where precise answer is needed – Yuriy Zaletskyy Apr 24 '15 at 13:45
  • Ok, I just thought there might be a smart project or an academic research where people tried to teach the machine to integrate instead of coding the algorithm on their own. Using NN to integrate seemed to be an interesting idea because the non-NN integration implementations need a lot of computing power. Now it is clear to me that NN are not necessarily the best solution for this problem. Thanks! – Mateusz Piotrowski Apr 24 '15 at 14:37
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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.

Sport
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fatachu
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    The OP seems to be asking about undefined integrals, like the integral of x^2 is x^3/3 – IVlad Apr 24 '15 at 14:06