Matrix-Multiplication CoefficientFunction * NumPy

Hi,

currently I am trying to integrate some TensorFlow neural Networks into NGSolve models for nonlinear mechanics. Basically I want to remodel the Nonlinear Elasticity Example but instead of using some closed formula I want to use my trained Neural Network to compute the Potential (W) from the material deformation (The Green-Langrangian Deformation tensor E).

Now I figured I cannot use my Network directly to create a function, that NGSolve can compile, but instead I need to remodel my Network using the weight matrizes and activation functions. The problem I now have is the twofold:

I want to multiply a vector (lets say size 6) and a weight matrix (lets say size 6*32) to return a vector of size 32. The vector is a CoefficientFunction and the matrix is a (constant) numpy array. I tried using the python (numpy?) operator for matrix multiplication The Operator used in the NGSolve example to create the right ChaucyGreen tensor The numpy matrix multiplication method and tensorproduct method The NGSolve method, all resulting in various errors.

I have attached my trial file so you can better understand, what I want to do.

I hope you can give me some hints how to solve my problem.

Thanks a lot!!

Best,
Til

Hi,
Vector and matrix valued CoefficientFunctions can be created using python tuples. If you use lists, domainwise coefficients are created, see:
ngsolve.org/docu/nightly/i-tutorials/uni...ficientfunction.html

Your symbolic form should be scalar though.

Best
Christopher

Hi Christopher,

that helped me a lot, thank you for your quick answer!
I just tried to get it working on a first multiplication, so my symbolic form is getting scalar in the end.

Best,
Til

Hi,

I am sorry that I have to ask some questions again...
While all the Computation itself works perfectly fine, I encountered some problems when trying to compute the stresses as derivatives of the Potential, when trying to compute the derivative of the Potential computed by Matrix-Multiplication I get the following error: I tried to look further into this, but W seems to get computed just fine from the GridFunction, the point where it starts to make problems is the differentiation and trying to get into the Diff function in debuging does not work. I am also not really getting ahead of the error message since at no point in the computation itself two matrizes with these dimensions get multiplied (what would be a problem) they just get summed up (what would be no problem (i guess?)).
I attached a sample file with some dummy values for the matrices so its easier to send those values, but the error stays the same no matter what are the values in the matrices.
So in the end my question would be what did I do wrong to cause this error?

I hope this is not just some rather obvious mistake I made on the computation itself and I am more than grateful for all the help I got here so far

Best,
Til

Hi Til,

it was a bug in the differentiation of the vectorized exp(.) function (and others).
It's fixed in the coming nightly.

Thanks for reporting the issue.

Joachim

Hi Joachim,

thanks for the fast reply I will install the nightly and be happy that everything works flawlessly.

Best
Til