  We present the application of a class of deep learning, known as Physics
Informed Neural Networks (PINN), to learning and discovery in solid mechanics.
We explain how to incorporate the momentum balance and constitutive relations
into PINN, and explore in detail the application to linear elasticity, and
illustrate its extension to nonlinear problems through an example that
showcases von~Mises elastoplasticity. While common PINN algorithms are based on
training one deep neural network (DNN), we propose a multi-network model that
results in more accurate representation of the field variables. To validate the
model, we test the framework on synthetic data generated from analytical and
numerical reference solutions. We study convergence of the PINN model, and show
that Isogeometric Analysis (IGA) results in superior accuracy and convergence
characteristics compared with classic low-order Finite Element Method (FEM). We
also show the applicability of the framework for transfer learning, and find
vastly accelerated convergence during network re-training. Finally, we find
that honoring the physics leads to improved robustness: when trained only on a
few parameters, we find that the PINN model can accurately predict the solution
for a wide range of parameters new to the network---thus pointing to an
important application of this framework to sensitivity analysis and surrogate
modeling.
