How to forecast time series if the training sample is a set of non-stationary series with different distribution parameters?

Question

Machine learning

Привет, обитателям хабра.

Стоит задача прогнозирования реального физического процесса с помощью ML.

Процесс может протекать по разному, все зависит от условий, в которых начинает моделироваться процесс и какие воздействия оказывались на процесс в период его протекания. Сезонность не наблюдается.

Уже реализовано моделирование процесса с помощью разностных схем, по проблема в том, что обсчёт происходит без ускорения, то есть реальном времени, что не позволяет делать прогнозы о протекании процесса в будущем. Возможность ускорить обсчет тоже нет, так как накладывается ограничение Куранта.

В результате, у меня есть множество нестационарных временных рядов с разными параметрами распределения, которые получили в результате обсчёта разностных схем.

Using ML methods, it is necessary to solve the problem of predicting the course of the process. As a training sample, a set of simulated time series.

On the Russian-speaking expanses of the Internet, I did not find how to solve such a problem, so I hope for you, Khabarovsk residents.

Answer 1

It is clear that non-stationary series are much more difficult to predict than non-stationary ones. There are different approaches. Starting with the classics - models in which there is a preliminary differentiation of the value of the series - the same ARIMA, in particular.
Another approach is dynamic row fragmentation, where you search for such fragments within which the properties of the row are stored. Modifications of that approach on the stream model of the series (the same change point detection methods) allow this to be done in real time.
If we talk about the use of modeling methods in this task, then they work on the principle of a "sliding window", when a forward forecast is made on the sample for the last period, then the forecast is compared with the actual incoming data and, by forecasting error, either continue to use the old model or rebuild it . The next question is which model are you using. And what is the nature of the data you are working with - there are no universally "good" models by definition. Moreover, non-stationary series can be very, very different, and for each task you need to look for and select your own approach. Many on this candidate's work do, by the way.
I strongly disagree with the fact that there are few sources on the Internet. Of course, there are not as many of them in the Russian-language fragment as in the English-language one - you can also find a couple of hundred links to articles and sites.