Optimization

The previous tutorials illustrated the use of NEML2 constitutive models in the "feed-forward" setting, i.e., the model maps from input variables to output variables with a given parametrization, i.e.

$$y=f(x;p,b).$$

Recall that $p$ and $b$ are respectively the parameters and the buffers of the model.

Another interesting use of NEML2 constitutive models is parameter calibration: With given input variables $x$, find the optimal parameter set $p^{\ast }$ such that

$$p^{\ast }=\underset{p}{\mathrm{argmin}}l(f(x;p,b)),$$

where $l$ is oftentimes referred to as the loss (or objective) function defining optimality.

This set of tutorials demonstrate the use of PyTorch Autograd to calculate parameter derivatives ( $\frac{\partial l}{\partial p}$), which is a necessary ingredient in all gradient-based optimizers.

• Automatic differentiation
• Parameter calibration