A Physics-Informed Neural Network Approach to Solution and Identification of Biharmonic Equations of Elasticity

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