preliminary version of DP NS example, not fully working so far

diffphys.md

@@ -300,6 +300,8 @@ By default DL frameworks store the internal states for every differentiable oper
 If we take a step back and look at $p = (\nabla^2)^{-1} b$, it's gradient $\partial p / \partial b$
 is just $((\nabla^2)^{-1})^T$. And in this case, $(\nabla^2)$ is a symmetric matrix, and so $((\nabla^2)^{-1})^T=(\nabla^2)^{-1}$. This is the identical inverse matrix that we encountered in the original equation above, and hence we can re-use our unmodified iterative solver to compute the gradient. We don't need to take it apart and slow it down by storing intermediate states. However, the iterative solver computes the matrix-vector-products for $(\nabla^2)^{-1} b$. So what is $b$ during back-propagation? In an optimization setting we'll always have our loss function $L$ at the end of the forward chain. The back-propagation step will then give a gradient for the output, let's assume it is $\partial L/\partial p$ here, which needs to be propagated to the earlier operations of the forward pass. Thus, we can simply invoke our iterative solve during the backward pass to compute $\partial p / \partial b = S(\partial L/\partial p)$. And assuming that we've chosen a good solver as $S$ for the forward pass, we get exactly the same performance and accuracy in the backwards pass.
 
+If you're interested in a code example, the [differentiate-pressure example]( https://github.com/tum-pbs/PhiFlow/blob/master/demos/differentiate_pressure.py) of phiflow uses exactly this process for an optimization through a pressure projection step: a flow field that is constrained on the right side, is optimized for the content on the left, such that it matches the target on the right after a pressure projection step.
+
 The main take-away here is: it is important _not to blindly back-propagate_ through the forward computation, but to think about which steps of the analytic equations for the forward pass to compute gradients for. In cases like the above, we can often find improved analytic expressions for the gradients, which we can then compute numerically.
 
 ```{admonition} Implicit Function Theorem & Time