Origami folds

Homogenization process from [Lebée et al, 2017]

Collaboration with A. Lebée and H. Nassar on Origami folds with applications in material science to study metamaterials.

The homogenization process above was introduced in [Lebée et al, 2017]. It leads to a system of constrained nonlinear PDEs. I work on proving existence and uniqueness of the solutions of those PDEs and on developing numerical methods to approximate them.

Phase-Field for fracture

3 point bending test

Using non conformal discretizations to improve the efficiency of phase-field computations for fracture. Collaboration with B. Bourdin.

Machine Learning

A neural net

The crux is to determine the optimal number of layers as well as the optimal numer of dofs.

Results of the stochastic gradient descent to train a neural net.

Making sure the training dataset is not overfitted.

Collaborations with non mathematicians to harness the power of machine learning and get predictive results even without a solid physical model. Collaborations include Pennington Biomedical Research Center and LECOR (Equine Orthopaedics at LSU).