To answer your questions directly, first:

Is there a decision tree regression model good when 10 features are
high correlated?

Yes, definitely. But even better than decision trees, is many decision trees (RandomForest, Gradient Boosting (xGBoost is popular). I think you'd be well served by learning about how decision trees split, and how they naturally deal with collinearity. Maybe try this video Follow the logic until the 2nd tier of splits, and you'll be able to imagine how the correlated variables are suddenly not important because they're relative to the split above them.

Is there a scientific or math explanation or recommendation (to use
decision tree regression)?

The math explanation of why collinearity is "bad" for linear models, comes down to the coefficients and how you interpret them. One of the side effects is that they can undermine the statistical significance of a variable, as well as flip their coefficients the wrong direction. It usually doesn't affect the accuracy of the model very much, but most people want linear models so that they can interpret the coefficients (which is totally messed up with collinearity). I suggest reading maybe this article to start.

One of the things that you mentioned, `include all variables if possible?`

is not really something you should be concerned with. The goal of a model is to explain the most, with the least. If you're forcing as many variables as possible into the model, then it's possible that you'll be fooled into thinking a model is good, when in fact it isn't if you were to test it on new data. In fact, sometimes less variables will give you a better model. This is exactly the kind of problem that multicollinearity causes with linear models - that you can't really judge very well what variables are significant or not. Stepwise selection doesn't work very well when there are correlated features.

In general, I think decision trees - especially Random Forests - will be a good start for you. But remember not to force all of the variables into the model just for the sake of it. Experiment with using less variables and manipulating the tree structure such as leaf size and max depth. And as always - test your model on validation data and holdout data so that you don't overfit a model and fool yourself into thinking it's a strong model.

problem: I have a dataset of about 30 columns. 10 columns have a high correlation with the target/dependend variable. High correlation has nothing to do with modeling here. – Subhash C. Davar – 2020-07-24T23:44:38.827

cor relatedness between probable features is a good basis for classification problem. It is not clear what prompts you to opt for decision tree model. It is based on linear modeling (lm). linear Regression need not be confused with simple linear models that are essentially based on data for correlated features. – Subhash C. Davar – 2020-07-25T00:00:55.833

For linear models it´s important to know correlated features. To handle this with VIF. The background of this question was, that I would like to do a prediction of numerical values. However include all variable. Not to kick out any variable with a VIF for linear models (neural net, multipl/regression). At the end I would like to play with all variables (features) to see the behavior, when changing values. Im looking from a engineering perspective. Im not interested just to get a good prediction. Target is a model for "playing" with features to derive information, how component could behav – martin – 2020-07-25T14:22:04.130

with that information, im going to change/optimize the structure of a component in engineering software. Data are out of machine tests. I cant see all properties in engineering software. With real world data and software Im optimizing. Hope I could explain it well. That´s the reason, why I want to know: Why can you use decision tree regression without kicking any correlated features like normal regression model or neural net. – martin – 2020-07-25T14:31:20.547

In your , step-regression analysis could be useful. Decision tree modeling has a different orientation and a separate purpose. – Subhash C. Davar – 2020-07-25T14:33:21.843

Would you recommend to do: decision tree regression model include all features (even the 10 high correlating features) to get a model for my purpose? Because multicollinearity has no effect in decision tree regression model? – martin – 2020-07-25T14:49:10.097

what I understand from Josh´s answer is, that it is possible to do that. Sorry it´s really a strange question from my point of view. – martin – 2020-07-25T14:52:16.823

I do not know about Decision tree regression. I have a rethinking . Given your problem, you can consider one of 6 variants of GAM models to cope with your issue of including all variables in your study.. Do not get scared with multicolinearity. IF necessary, transform your data variables to safeguard against so called multicolinearity. – Subhash C. Davar – 2020-07-25T15:29:47.683

Ah yes I know about poisson and some of these processes. Thank you very much I going to learn about that. What do you mean with transform to safeguard? Something like normalization min max? – martin – 2020-07-25T20:28:14.550

I do not know about your data types. could you send a part of it - a sample. Right now, I have "standardization" in my mind to realize best and valid model. – Subhash C. Davar – 2020-07-26T02:02:23.313

subhash C. Davar is available on stats.stackexchange.com with a score of 1. – Subhash C. Davar – 2020-07-26T02:04:50.220