  This work applies concepts of artificial neural networks to identify the
parameters of a mathematical model based on phase fields for damage and
fracture. Damage mechanics is the part of the continuum mechanics that models
the effects of the micro-defect formation using state variables at the
macroscopic level. The equations that define the model are derived from
fundamental laws of physics and provide important relationships between state
variables. Simulations using the model considered in this work produce good
qualitative and quantitative results, but many parameters must be adjusted to
reproduce a certain material behavior. The identification of model parameters
is considered by solving an inverse problem that uses pseudo-experimental data
to find the values that produce the best fit to the data. We apply a
physics-informed neural network and combine some classical estimation methods
to identify the material parameters that appear in the damage equation of the
model. Our strategy consists of a neural network that acts as an approximating
function of the damage evolution with its output regularized using the residue
of the differential equation. Three stages of optimization seek the best
possible values for the neural network and the material parameters. The
training alternates between the fitting of only the pseudo-experimental data or
the total loss that includes the regularizing terms. We test the robustness of
the method to noisy data and its generalization capabilities using a simple
physical case for the damage model. This procedure deals better with noisy data
in comparison with a PDE-constrained optimization method, and it also provides
good approximations of the material parameters and the evolution of damage.
