A problem I'm currently working on requires me to optimize some dimension parameters for a structure in order to prevent buckling while still not being over engineered. I've been able to solve it use iterative (semi-brute forced) methods, however, I wondering if there is a way to implement a gradient descent method to optimize the parameters. More background is given below:
Let's say we are trying to optimize three length/thickness parameters, (t1,t2,t3) . We initialize these parameters with some random guess (t1,t2,t3)g. Through some transformation to each of these parameters (weights and biases), the aim is to obtain (t1,t2,t3)ideal such that three main criteria (R1,R2,R3)ideal are met. The criteria are calculated by using (t1,t2,t3)i as inputs to some structural equations, where i represents the inputs after the first iteration. Following this, some kind of loss function could be implemented to calculate the error, (R1,R2,R3)i - (R1,R2,R3)ideal
My confusion lies in the fact that traditionally, (t1,t2,t3)ideal would be known and the cost would be a function of the error between (t1,t2,t3)ideal and (t1,t2,t3)i, and subsequent iterations would follow. However, in a case where (t1,t2,t3)ideal are unknown and the targets (R1,R2,R3)ideal (known) are an indirect function of the inputs, how would gradient descent be implemented? How would minimizing the cost relate to the step change in (t1,t2,t3)i ?
P.S: Sorry about the formatting, I cannot embed latex images until my reputation is higher.