Data-Driven Computing in Elasticity via Chebyshev Approximation

This repo consists of all the codes and dataset of the research paper, "Data-driven computing in elasticity via Chebyshev Approximation". Code heavily borrowed from Prof. Yoshiro Kanno's Matlab Code.

Abstract :

This paper proposes a data-driven approach for computing elasticity by means of a non-parametric regression approach rather than an optimization approach. The Chebyshev approximation is utilized for tackling the material data-sets non-linearity of the elasticity. Also, additional efforts have been taken to compare the results with several other state-of-the-art methodologies.

Keywords :

Data-driven computational mechanics, Model free method, Nonparametric method, Chebyshev polynomials, elasticity, Chebyshev approximation, chebfun

Authors :

Rahul-Vigneswaran K^∗, Neethu Mohan^† and Soman KP^†.

^∗Department of Mechanical Engineering, Amrita Vishwa Vidyapeetham, India.
^†Center for Computational Engineering and Networking (CEN), Amrita School of Engineering, Coimbatore.

How to use the code?

1. Clone this repository.
2. For Kernal Regression :
   1. Enter the Kernal Regression directory.
   2. Run cross_valid.m.
   3. Run truss_analysis.m.
3. For Chebyshev Approximation :
   1. Install Chebfun library.
      1. Install from the official website (or) use the library (chebfun directory) included in this repository. (Open an issue if you have trouble with this part)
   2. Enter the Chebyshev Approximation directory.
   3. Run truss_analysis.m.
4. For Polynomial Fitting 8 degree :
   1. Enter the Polynomial Fitting 8 degree directory.
   2. Run truss_analysis.m.
   3. To change the degree of the polynomial fit, open truss_analysis.m and follow the instructions given in the comments.
5. For Single Layered Neural Network :
   1. Enter the Single Layered Neural Network directory.
   2. Run truss_analysis.m.
   3. To change the architecture of the Neural Network, edit the file NN_5.m and replace it with your architecture in a similar format as given in it by default.

Recommended Citation :

If you use this repository in your research, cite the the following papers :

1. Rahul-Vigneswaran, K., Mohan, N., & Soman, K.P. (2019). Data-driven Computing in Elasticity via Chebyshev Approximation. CoRR, abs/1904.10434..
2. Kanno, Y. (2018). Data-driven computing in elasticity via kernel regression..

Bibtex Format :

@article{RahulVigneswaran2019DatadrivenCI,
  title={Data-driven Computing in Elasticity via Chebyshev Approximation},
  author={K Rahul-Vigneswaran and Neethu Mohan and K. P. Soman},
  journal={CoRR},
  year={2019},
  volume={abs/1904.10434}
}

@inproceedings{Kanno2018DatadrivenCI,
  title={Data-driven computing in elasticity via kernel regression},
  author={Yoshihiro Kanno},
  year={2018}
}

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Issue / Want to Contribute ? :

Open a new issue or do a pull request incase your are facing any difficulty with the code base or you want to contribute to it.