Physics-constrained symbolic model discovery for polyconvex incompressible hyperelastic materials (Q6589318)

A machine learning framework of inferring hyperelastic energy functionals for incompressible materials from sparse experimental data and physical laws is proposed in this paper. One central ingredient is the introduction of a polyconvex neural additive model (PNAM), which enables the expression of the hyperelastic model in a learnable feature space while enforcing polyconvexity. Genetic programming is applied to further improve interpretability. The machine learning-based model presented in this paper is proved to require fewer arithmetic operations than its deep neural network counterparts in employment.