How to use sobol analysis in a 2d model with time-dependent response?

Hello, guys! I am starting to use UQ Lab and i would like some help with these issues.
First of all, i have a matlab model, that receive a time vector and give me the 2d output, position and velocity as a unique vector 1x2.
I would like to run the sensitivity analysis on this model. There are 9 variables and i am not sure about the relations of dependence.
I already implemented my model and when I use the module uq_evalModel the response is ok, but when I run the sobol analysis, the sobol indices are negatives and the total indice value is greater than one.
I am having problems with the sample size too. If my model received a time vector of 400 points, Should the sample size be iqual? I would appreciate some help.

Hi @Thamires_Viana

Welcome to UQWorld! :slight_smile:

Perhaps you can tell me more about your problem.

So you have a time-dependent model with 9 variables involved. Is time, by any chance, a part of those 9 variables? While technically time is an input of your MATLAB model, it might not necessarily be part of the inputs in your sensitivity analysis. This is related to your last problem as well, because you mentioned sample size and the time vector; did you randomly generate these time points?

In sensitivity analysis of time-dependent problems, it is often the case that time is not considered an input but a parameter. That is, the time point you’re interested in is already fixed in advance; if you are interested in many points (say, 400 points) you simply have a model with multiple outputs (400 \times 2 = 800 outputs, that is). It is quite common as well to summarize such a high-dimensional output in terms of a few features (max., min., etc.).

Finally, the dependence relations between the input variables are of course depends from case to case, without more information I don’t think anyone can help you with that. As a starting point, you can always model your inputs as independent inputs.

Thank you for your reply! Your insight about the time vector helped me to identify the issue of my code. As you said, the time vector was an input and correcting this point, I had no problems with the sample size anymore.
About the dependence relations, I am studying more the problem and for now the relations are as independent inputs.

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Hi @Thamires_Viana,

Thanks for the feedback. I’m glad to hear that! If you run into some other issues, feel free to open a new topic here. Some of us (I included) would be happy to help you.