🧠 PINN vs FEM
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Deflection — three solvers, one beam
Closed form (truth)
FEM (Hermite cubics)
Neural network
Training loss
Potential energy → the exact minimum
Bending moment
Error vs the closed form
Beam
Supports
Cantilever
Simply supported
Distributed load q (N/m)
1200
Point load P (N)
0
Its position (x/L)
0.60
FEM elements
4
Network
Formulation
Energy (Deep Ritz)
Residual (classic PINN)
Width
16
Depth
2
Learning rate
0.010
Hard boundary conditions
Train
Reset
Results