# Predicting evolution of an unknown mathematical function with machine learning?

Is it possible to predict how a mathematical function evolves using ML? I am studying radioactive decay of polonium 210 and I have gathered data for its decay throughout a couple of weeks. I was wondering if I could use Machine Learning to train on the data available and predict how the Radioactive Activity would evolve after the timeframe where I gathered data. Can I predict (with ML) how the radioactive activity would evolve based on available experimental data?

## 1 Answer

You don't need any ML to do this task. If you search on Wikipedia Radioactive Decay you will lear in the "decay rate" section that there is a known behaviour of the times of the decays. In particular the decay of a radioactive nuclide follows what is called a Poisson process, hence the number of events in a given time window follows a Poisson distribution and the delay between two consecutive events follows an exponential distribution with a mean value that is the inverse of the decay constant. As you have the timestamp of each decay event you can calculate the delays between them and fit with an exponential distribution to obtain the decay rate of Po210. Otherwise you can calculate the number of events in a given time window and using the Poisson hypothesis you can calculate the same value for the decay rate.

As the radioactive decay is a true random event that follows quantum physics rules you won't be able (in any possible way) to know when the process wi take place, you can only estimate the probability that it will take place in a given window of time.