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).