update SoL code

diffphys-examples.md

@@ -1,23 +1,23 @@
 Complex Examples Overview
 =======================
 
-The following two sections with show code examples of two more complex cases that 
-will show what can be achieved via differentiable physics training.
+The following sections will give code examples of more complex cases to 
+show what can be achieved via differentiable physics training.
 
-First, we'll show a scenario that employs deep learning to learn the errors
-of a numerical simulation, following Um et al. {cite}`um2020sol`.
+First, we'll show a scenario that employs deep learning to represent the errors
+of numerical simulations, following Um et al. {cite}`um2020sol`.
 This is a very fundamental task, and requires the learned model to closely
 interact with a numerical solver. Hence, it's a prime example of 
 situations where it's crucial to bring the numerical solver into the 
 deep learning loop.
 
 Next, we'll show how to let NNs solve tough inverse problems, namely the long-term control
-of a fluid simulation, following Holl et al.  {cite}`holl2019pdecontrol`. 
+of a Navier-Stokes simulation, following Holl et al.  {cite}`holl2019pdecontrol`. 
 This task requires long term planning,
 and hence needs two networks, one to _predict_ the evolution, 
-and another one to _act_ to reach the desired goal. 
+and another one to _act_ to reach the desired goal. (Later on, in {doc}`reinflearn-code` we will compare
+this approach to another DL variant using reinforcement learning.)
 
 Both cases require quite a bit more resources than the previous examples, so you 
-can expect these notebooks to run longer (and it's a good idea to use the check-pointing
-mechanisms when working with these examples).
-
+can expect these notebooks to run longer (and it's a good idea to use check-pointing
+when working with these examples).