Which part of the FEM model do you want to train, (i) constitutive equations (ii) basis functions, (iii) matrix/vector computations, (iv) matrix solver?

Not many seem to understand the difference between a curve-fitting technique for a known data and a numerical method for solving PDEs. FEM is not a curve-fitting technique. It is a numerical method for solving PDEs.

So, a more important question: is it worth using ML for FEM, or for any numerical method aimed at solving PDEs?

Wherever possible, FEM models should always be "calibrated" using experimental data. The attached list of relevant references may be of assistance,

Schwarz B.J. and Richardson M.H. (1999). Experimental Modal Analysis, Proc. CSI Reliability Week, Orlando, Florida, October 1999.

Ewins D.J. (1999). Modal Testing: Theory, Practice & Application (2nd Edition), Research Studies Press, Hertfordshire, UK, 415-515.

Dascotte E. (2004). Linking FEA with Test, , Sound and Vibration, April 2004, 12-16.

Hopkins R.N., Carne T.G., Dohrmann C.R., Nelson C.F. and O’Gorman C.C. (2004). Combining Test-Based and Finite Element-Based Models in NASTRAN, Sound and Vibration, April 2004, 18-20.

Lang G.F. (2005). Experimental FEA…Much More Than Pretty Pictures, Sound and Vibration, January 2005, 12-20.

Ancich E.J. (2007). Dynamic Design of Modular Bridge Expansion Joints by the Finite Element Method, Proc. International Association for Bridge & Structural Engineering

(IABSE) Symposium, Weimar, Germany.

Morassi A. & Tonon S. (2008). Dynamic Testing for Structural Identification of a Bridge, J. Bridge Engineering, ASCE, 13(6), 573-585.

Thank you Eric Ancich for your answer. Actually, I mean training FEM models using machine learning methods based on experimental results, rather than just verifying them.

this is site may be can help you

Article A finite element-based machine learning approach for modelin...

Dear Faezeh Iranmanesh

This papers exactly answers your question

Article A deep learning approach to estimate stress distribution: a ...

https://arxiv.org/ftp/arxiv/papers/1801/1801.07337.pdf

Thank you Ammar Alkinani

Thank you Sourangshu Ghosh

My little contribution: Article Full field optical measurements in experimental modal analys...

Best regards,

Alessandro

Which part of the FEM model do you want to train, (i) constitutive equations (ii) basis functions, (iii) matrix/vector computations, (iv) matrix solver?

Not many seem to understand the difference between a curve-fitting technique for a known data and a numerical method for solving PDEs. FEM is not a curve-fitting technique. It is a numerical method for solving PDEs.

So, a more important question: is it worth using ML for FEM, or for any numerical method aimed at solving PDEs?

Faezeh Iranmanesh

Very simply put, you are trying to solve an inverse problem, i.e. a problem of the kind where you know the answer to be four but have to answer - what is the question.

Perhaps some of the below adds insight to the problem?

https://qringtech.com/learnmore/why-simulate-measure-correlate-automate/

Presentation Analysis Technology:; A discussion on some of the fundamentals

Article 2005-01-2342 NVH optimization of truck cab floor panel embos...

Article FE Model Correlation & Mode Shape Updating using Qualificati...

As the above shows - just tweaking a model input for a best fit is not always meaningful for a variety of reasons.

Sincerely

Claes

FEA does usually not give any damping, so damping can be added from modal analysis meaurements with fitted data. FEA also have limitations regarding the frequency range: Works best for the lowest frequencies and regions of low modal density. When the modal density surpasses a given value, statistical energy analysis (SEA) is a better approach. However tools with both theories are available now.

Hi Anders Buen

I am not trying to demote the usefulness of QA in the form of Test/FE.

However, it is far from as straightforward that it at first may seem, e.g. when two tests made at different amplitude do not reveal the same answer (see the FE Model correlation paper) or when differences between actual (Test) and assumed (FE) geometry matters (see NVH optimization paper).

To make things even more fun - feeding two FE software identical models does not produce identical results. Apparently this may stem from differences in how the FE solvers operate in the matrix. Great fun to be had in trying to decide which one is true. (See the Analysis Technology presentation).

As the saying goes - inverse, easily become perverse. A better approach therefore is a so called forward approach, i.e. tweak model FE data for a best fit. This approach, however, is unable to reveal true errors in the assumptions the FE model rest upon and these tend to matter.

In my experience, SEA rarely produce more accurate results than does FE. However, SEA is more lightweight and is the tool one has to use when modelling large systems at high frequency, i.e. when modelling objects where wavelength is small as compared with object size.

SEA has its own set of demons, see this paper for an example of a rather important system error in the SEA method plus a first stab at correcting it (it is peer reviewed).

Conference Paper A Modification of the SEA Equations: A Proposal of how to Mo...

/Claes

Dear Faezeh,

There is a book entitled - "Practical Inverse Analysis in Engineering", from David Trujillo and Henry Busby. It may be useful.

In my case I was interested in the inverse problem for determining the loads by using FEA and Strain Gage Measurements.

Hope it helps,

Regards,

Giovanni.

SEMM Steven Klaassen

Dear Faezeh Iranmanesh

The reverse finite element approach is the best way that can be employed to do this. I've used this technique to extract cap model and brain hyperelastic parameters in the powder compaction process and human brain indentation respectively. Also, it can be used for a great variety of engineering experiments.

In fact, this question is very difficult to answer.

The core of machine learning is to construct the loss function and get the optimal result. If the input condition is the result obtained by FEM, the physical significance of the constructed loss function is not clear.

The uncertainty of doing so is too large, which is rooted in the FEM algorithm (constitutive, model precision, etc.), and also includes the error transfer process.

That's my understanding. I hope it's helpful

Finding parameters of a FEM model using known measurements is, in fact, an inverse problem and can be solved by using neural networks. You can see my work:

Book Inverse and Crack Identification Problems in Engineering Mechanics

Article Neural network assisted crack and flaw identification in tra...

A recent combination of FEM, with a constitutive law that is based on neural networks and a data-base of experiments has been done as well, see for example:

Article Data-driven Computational Homogenization Using Neural Networ...

Using neural networks in order to solve a problem described by PDEs is also possible, see the seminal contribution of @Isaac E. Lagaris Article Artificial neural networks for solving ordinary and partial ...

and many recent papers, using the description: physics informed neural networks.

I fully agre with majority of already provided answers. There are tons of publications using FEA predictions to mutch actual measurements to indirectly define unknown parameters of the model. In case of relatively simple linear problems with a few unknown parameters (e.g., stiffness parameters of components), this technique is routinely used by engineers using, for example, the least square method. For non-linear problems, more advanced matching techniques are used: Abaqus, for example, provide standard options to define parameters of hyper-elastic constitutive models. For more complex statements, well-establish inverse methods can be applied. As a typical example, Structural health monitoring (SHM) uses such matching (including both training and detection) to find damages and their parameters for risk assessment. You may want to google both “FEA” and “inverse problems” to see a portion of results in this direction.

Dear Faezeh

In my opinion, your question is related to the problem of finite element model updating. Generally, we can build any FE model based on the available information. Also, there are many commercial and non-commercial software that enable engineers to build any complex FE model. However, an important note is that this model may be different from its real or experimental model due to some idealizations and assumptions. Therefore, it is necessary to update this model by considering the experimental data acquired from the real system.

Having considered this concept, you can enter the world of machine learning. In this case, you should consider or use three main information (training data): (1) the analytical or numerical data related to the FE model, (2) the updating parameters, (3) the experimental data. Therefore, you can learn a machine learning algorithm using the mentioned information to update the FE model or its updating parameters. In this regard, the model updating is a supervised learning problem because both information of the FE and real systems are used to learn the machine learning model.