  We explore an application of the Physics Informed Neural Networks (PINNs) in
conjunction with Airy stress functions and Fourier series to find optimal
solutions to a few reference biharmonic problems of elasticity and elastic
plate theory. Biharmonic relations are fourth-order partial differential
equations (PDEs) that are challenging to solve using classical numerical
methods, and have not been addressed using PINNs. Our work highlights a novel
application of classical analytical methods to guide the construction of
efficient neural networks with the minimal number of parameters that are very
accurate and fast to evaluate. In particular, we find that enriching feature
space using Airy stress functions can significantly improve the accuracy of
PINN solutions for biharmonic PDEs.
