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Using gradient information in building surrogate models of CFD

Phil_Kay

Hi,

Not expecting a whole load of answers on this. I think it is a bit niche!

I presented to some engineers today on determining robust design solutions using DoE and Monte Carlo simulation experiments. One of the audience asked about krigging and when I asked him to elaborate it turned out that he meant something different to what I was thinking. I don't know a lot about CFD modelling but he told me that, in addition to getting the estimate of the response, they can also get some information about the gradient of the response surface for each run of the simulation. Not sure how this works but I can imagine it is useful information. How could they build this in to the surrogate model. See below for his description of the challenge.

The aspect I discussed with you was including gradient information in the construction of a response surface model. My interest is primarily in using DoE with Computational Fluid Dynamics (CFD) analyses where it’s usually necessary to limit the number of experimental points as much as possible to keep the overall computational cost under control. In the past I’ve used space-filling designs (such as Latin Hypercube) with CFD analyses with some success. However when the number of data points is quite low it’s not obvious that the response surface will adequately represent the convexity (shape) of the underlying data unless the data is quite smooth. Incorporating gradient information, as we’ve investigated with Prof Andy Keane in the Computational Engineering and Design Group at Southampton University, is one way of improving the ability of the response surface to represent the underlying shape of the data. One of our main CFD tools includes an adjoint capability, whereby solution of the adjoint equations derived from the Navier-Stokes equations used to represent the flow provides information on the sensitivity of engineering variables such as drag to changes in geometry or flow boundary conditions. This sensitivity information would seem to be a good candidate for improving the response surface defining the surrogate model.

Accepted answers

Bill_Worley

Sorry Phil, I had not heard of using gradient information before your question. I did a little research and it seems to have been around for at least a few years now. Wish I could be of more help here.

Bill

All comments

nick_shelton

Hi Phil,
I had an user with a similar interest, he was working with surrogate models for aircraft wing design.
We spent some time exploring JMP's "Gaussian Process" platform and we were able to build his model.
My recommendation would be to have them build a model with their variables of interest using "Gaussian Process" and evaluate the results.

Bill_Worley

Hey Phil,

I agree with Nick on the Guassian Process. Although I would recommend that they also try Neural Nets. We/I built many surrogate models while at P&G for similar CFD type applications and Neural Nets almost always came up with better predictive models.

I would also recommend that your customer try the Fast Flexible Filling MaxPro designs to better "fill" the design space. It will push design points closer to the corners/edges while still maximizing the minimum distance between points.

Bill

Phil_Kay

Thanks. Those all seem like good ideas.
Have you had any experience of using gradient information? This seems to be the key for my customer. As I say, I think it is a fairly unusual request.

Thanks again,
Phil

Bill_Worley

Bill

Phil_Kay

No worries, Bill. I thought it was a long shot that anyone would have used this approach!

Phil_Kay

In case anyone else is interested, I spoke to Chris Gotwalt about this last week while he was in the UK. He said that he is aware of the appraoch of using gradient information in building surrogate models for CFD to get a better model with fewer design points. However, this is not something that you can do in JMP. And it is not something that is likley to be added in JMP because it is a very niche application.

Thanks all for your comments.

Phil