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Solving Stochastic Ordinary Differntial Equation using PCE

Hi,

I would like to solve an ordinary stochastic differential equation using PCE. Is there any example to follow.

Thanks,
Ahmed

Hi @Ahmed_Atallah ,

Thanks for your interest in UQLab!

It depends on your stochastic ODE. Is it stochastic because one or several parameters are stochastic? In that case: The PCE module of UQLab uses the black-box approach, i.e., it is non-intrusive. Therefore, you can apply PCE in the same way that you would apply it to any other model: You specify an experimental design (in the random parameter space), compute model evaluations, and based on this data set you fit a PCE.

Is your quantity of interest a scalar or the whole time series? In the first case, it should be quite straightforward to solve. In the second case, maybe these discussions help you:

In case your ODE is stochastic because there is some stochastic process driving the evolution, your model might actually be a stochastic simulator. Then it is not straightforward to use PCE.

Hope this helps! :slight_smile: Feel free to give us more information about your model, inputs and outputs, and keep us updated about how you solve your problem.

Hi Nora,

Thanks so much!

I am interested in the non-intrusive approach. The problem I want to solve is the orbit problem which is an ODE. I want to propagate the uncertainty caused by the initial condition and some parameters.

Thanks,
Ahmed