I need to create a neural network that solves the elastic problem of a plate under load and I want to implement a physics informed neural network that solves the problem by minimizing a loss function based on the toal potential energy principle.

I used as loss function the total potential energy principle, that states that the equilibrium configuration of a structure is the one that minimize the total energy of the system. So I imposed that Loss function=minimum potential energy, I performed the integrations and then, in order to minimize it, I imposed that the derivative of the total potential energy itself with respect to the variable I want to recover is equal to 0. I obtain an equation of the type A*x=b in which x are the weights of the neural netwrok, but it doesn’t work. Maybe there is something wrong in the integration procedure or in the loss function construction.