# Is it possible to solve FEM by Neural Network?

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Alhaz Uddin on 25 May 2011
Commented: Akshat Rastogi on 10 Nov 2018
Spar platform is one type of floating structures applicable to deep and ultra deep water region for oil and gas exploration. It is a cylindrical deep draft floating hull, held in place by mooring lines anchored to the sea floor. Displacement along x, y and z axis of spar platform occurs due to wave and current effect and rotation with respect to x, y and z axis of platform due to same reason. Total 6 types of response (3 displacements and 3 rotations) have been obtained from analysis of spar platform by Finite Element Method (FEM) software. FEM is computationally very expensive and highly time consuming process. It is normally required 18~20 hours for getting each response.
Total 23 no. of inputs such as wave height, current speed, depth of water, diameter of spar, length of spar etc. have been used for analysis of spar platform by FEM.
And total 6 types of response (3 displacements and 3 rotations) have been obtained as output of FEM analysis. More than 2000 values for each response can be obtained in 1000 sec. by FEM.
I want to train an Artificial Neural Network (ANN) where FEM analysis inputs will be used as ANN inputs and target value will be as like output of FEM. After completing train of ANN, prediction of responses of spar platform will be done.
Is it possible to solve this type of problem by ANN?

Walter Roberson on 25 May 2011
Hmmm, maybe. My intuition is that if it can be done at all, it would require as many layers as the maximum nesting depth of integration or differentiation. I do not, however, have any intuition about how ANN would model the evolution of such a system over time.
Akshat Rastogi on 10 Nov 2018
Do you think its possible to learn the "Solver" of FEM using ANN? So that for any geometry, different Boundary conditions, Loads, etc....I'm able to compute the primary variable i.e. Displacement, Temperature etc.?

Adrien Leygue on 25 May 2011
This kind of problem is typically the case where one would use model reduction techniques. I would refer you to methods such as the proper orthogonal decomposition method or proper generalized decomposition.
The basic idea lies in the fact that if you look at your FEM solution for the many different inputs they will be somehow similar. Therefore one would be tempted to solve the FEM problem in a more appropriate basis able to reproduce the outputs with just a few degrees of freedom.
A neural network would kill you because of the many solutions you would need to train it.
Google the following keywords: Proper orthogonal decomposition (POD), Proper Generalized decomposition (PGD), reduced basis, ...
You can also have a look at this library: http://morepas.org/software/index.html
Hope this helps,
A.

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