2D Linear Elasticity via PINN

Obeyance of Navier-Cauchy equation by the PINN model for the collocation points
Obeyance of Navier-Cauchy equation by the PINN model for the collocation points
PINN, TensorFlow Hypercube Sampling, 2D linear-elasticity Lowest loss: 2.22 (6 layers, 15 neurons each)

Physics-informed NN for predicting the 2D linear elasticity parameters (Displacement, Shear-stress, BCs, laws) of an 1 sq. meter steel plate fixed at bottom under 4 Newton uniform vertical load. Reduce reliance on dense FEM labels and deliver fast, physics-consistent field predictions for design sweeps. TensorFlow PINN with Navier–Cauchy + Hooke residuals; Latin-hypercube sampling of collocation (1k inside, 50 each boundary) points; Dirichlet/Neumann BCs; 27-config hyperparameter sweep with validation tracking. Best topology (6×15, dropout 0.3, Glorot) identified via 27-config grid search; val loss 2.22 at 1k epochs (first LR stage). Full 10k-epoch run converged to training loss 0.53 — validation against exact analytical solution pending.

GitHub

Residuals
Residuals for the shear-stress components (point-wise) predicted by the PINN.
Neumann-BC
Residuals for the Neumann-BCs (point-wise) predicted by the PINN