# Parameterized geometry Linear Elasticity

Hello,
I am trying to solve the linear elasticity for parameterized geometry. My usecase is a cantilever beam where the length, breadth, height are varied. Thus the geometry has 3 parameters namely L, B and H. From the three-fin tutorial example, I see that the geometry dimensions are just added as additional features along with the spatial inputs namely (x,y,z) coordinates. Linear elasticity physics loss function needs to compute the gradients of displacement and stress with respect to the input. In our case, the inputs are (x,y,z,l,b,h)
If the geometry is definied as parameterized in Modulus, does it automatically apply the chain rule to compute the derivates?
for example if the output of the network is displacement u,
du/dx = du/dL * dL/dx + du/dw * dw/dx + du/dh * dh/dx
In other words, how are the dimensions of the geometry considered in the Physics residual loss computation thereby it generalizes.
Thanks

For learning systems with parameterized geometry using a point wise methods, our examples use a explicit parameterization where these params are model inputs as you mentioned. That means the output quantity is directly related to the current geometry. For the 3-fin example see the list of inputs here.

Because the inputs of the neural network are partly the geometry parameterizations, the PDE loss depends on them since they are used to calculate the state variable which is needed for gradients as well. While unlike the spatial point inputs, we may not have explicit gradients of these terms they still impact the optimization akin to normal data-driven training.