escipt for inverse problem

We have played around with escript and scipy for optimization but for some simple test cases. It would be interesting to see how things work for more complex problems. In fact we are working on tools to support optimisation/inversion (e.g. including symbolic differentiation) with a focus on geoscience applications.

Your questions:
* Can I project experimental displacement fields on a given unstructured mesh ?
I assume you want to interpolate gridded data to an unstructured grid, see http://esys.esscc.uq.edu.au/esys13/3.2/epydoc/esys.escript.escriptcpp.Data-class.html#interpolateTable.

* Is this possible to define large strain ?
As long as you can express this as a sequence of PDE solves (and mesh updates) there is - in principle - no problem. People have done these with escript.

* Can I couple equation with Lagrange multiplier to deal with incompressible materials like rubber ?
This is tricky business. You have two options:

   (a) use the iterative penalty method, eg. see (1.7) in http://www.google.com/url?sa=t&source=web&cd=9&ved=0CGAQFjAI&url=http%3A%2F%2Fgraduate.math.nus.edu.sg%2F~g0202184%2Fwork%2Fsrmcon.pdf&rct=j&q=penalty%20method%20navier%20stokes&ei=uLO4TeixH426vQPLx-miAw&usg=AFQjCNHGtiI5RfGLTEmXNTbkI7E39_PkcQ&cad=rja. this has been successfully applied in escript for a lot of problems but as the stiffness matrix tends to be ill conditions a direct solver needs to be used which in most cases limit the application to 2D. But it is simple to implement.

   (b) use mixed FEM. escript/finley support macro elements (even on unstructured meshes) to approximate pressure. An implementation for a solver is http://esys.esscc.uq.edu.au/esys13/3.2/epydoc/esys.escript.rheologies.IncompressibleIsotropicFlowCartesian-class.htm which may require modifications to run this for your problem.

* Can I easily extract sub regions of the mesh for the optimisation process ?
I need to know exactly what you want to do.

* Is this possible to use lazy evaluation to find the best relaxation parameters for Newton optimization algorithm ?
Can you explain a bit more what the issue is?

> Lutz Gross proposed the following answer:

> We have played around with escript and scipy for optimization but for

> some simple test cases. It would be interesting to see how things work

> for more complex problems. In fact we are working on tools to support

> optimisation/inversion (eg including symbolic differentiation) with a

> focus on geoscience applications.

Ok so if you are working on such tool, may be we can have some private
discussion to join our forces, I have done my PhD on this subject, so I can
help.

> * Can I project experimental displacement fields on a given unstructured
> mesh ?

> I assume you want to interpolate gridded data to an unstructured grid,
> see
> http://esys.esscc.uq.edu.au/esys13/3.2/epydoc/esys.escript.escriptcpp.Data-class.html#interpolateTable.

Ok, thanks

> * Is this possible to define large strain ?

> As long as you can express this as a sequence of PDE solves (and mesh
> updates) there is - in principle - no problem. People have done these
> with escript.

Fine.

> * Can I couple equation with Lagrange multiplier to deal with
> incompressible materials like rubber ?

> This is tricky business. You have two options:

> (a) use the iterative penalty method, eg. see (1.7) in
> http://www.google.com/url?sa=t&source=web&cd=9&ved=0CGAQFjAI&url=http%3A%2F%2Fgraduate.math.nus.edu.sg%2F~g0202184%2Fwork%2Fsrmcon.pdf&rct=j&q=penalty%20method%20navier%20stokes&ei=uLO4TeixH426vQPLx-miAw&usg=AFQjCNHGtiI5RfGLTEmXNTbkI7E39_PkcQ&cad=rja.
> this has been successfully applied in escript for a lot of problems but
> as the stiffness matrix tends to be ill conditions a direct solver needs
> to be used which in most cases limit the application to 2D. But it is
> simple to implement.

> (b) use mixed FEM. escript/finley support macro elements (even on

> unstructured meshes) to approximate pressure. An implementation for a

> solver is

> .IncompressibleIsotropicFlowCartesian-class.htm"
> target="_blank">http://esys.esscc.uq.edu.au/esys13/3.2/epydoc/esys.escript.rheologies

> .IncompressibleIsotropicFlowCartesian-class.htm which may require

> modifications to run this for your problem.

Thanks, for the be method I already show it, but it deals with flow, I'm
not sure it can be easily adapted for anisotropic hyperelastic damage laws.

> * Can I easily extract sub regions of the mesh for the optimisation
> process ?

> I need to know exactly what you want to do.

When you solve inverse problem using full field measurement you can't have
the whole specimen observed. So you have two options, you can choose to use
a simplified model as plan stress/strain and directly use the experimental
displacement boundaries as dirichlet condition, or you can model your whole
specimen and applying measured forces, and updating the model you want to
fit using the kinematic full field measured region. The last method is of
course the best, but it's more complex to implement, that's why it is
needed to extract a submesh on a given region, where the optimization
problem will be solved

> * Is this possible to use lazy evaluation to find the best relaxation
> parameters for Newton optimization algorithm ?

> Can you explain a bit more what the issue is?

You can have a lot of bias that you want to avoid, for example I have
solved an inverse 3D heat transfer problem in my older lab where I have to
determine the exchange coefficient and the conductivity of the material.
This values doesn't have the same sensitivity, so I have to relax each
parameter with a given value manually tuned. I think it can be much more
efficient to determine this coefficient using a symbolic approach allowoing
by lazy evaluation.

Best Regards

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> * Can I easily extract sub regions of the mesh for the optimisation
> process ?
there is no support for sub-meshes as such but you can solve a suitable dummy problem on the region you are not interested in.

> * Is this possible to use lazy evaluation to find the best relaxation
> parameters for Newton optimization algorithm ?
lazy evaluation is not a symbolic tool box but this is what we are currently working on.