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Physics informed neural network for approximating the deformed shape of a beam

We consider a beam on two supports and with a distributed load.

We approximate the numerical solution of the differential equation of the beam with a neural network.
We use the Jax library for machine learning.

Evolution of loss function components during training of the PINN:
losses

Comparison of the numerical approximation obtained with the PINN, and the analytical solution of the beam deflection:
deformed shape