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diffphys-outlook.md

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 Summary and Discussion
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-The previous sections have explained the differentiable physics approach for deep learning, and have given a range of examples: from a very basic gradient calculation, all the way to complex learning setups powered by simulations. This is a good time to pause and take a step back, to take a look at what we have: in the end, the _differentiable physics_ part is not too complicated. It's largely based on existing numerical methods, with a focus on efficiently using those methods to not only do a forward simulation, but also to compute gradient information. What's more exciting is the combination of these methods with deep learning. 
+The previous sections have explained the differentiable physics approach for deep learning, and have given a range of examples: from a very basic gradient calculation, all the way to complex learning setups powered by complex simulations. This is a good time to pause and take a step back, to take a look at what we have: in the end, the _differentiable physics_ component of these approaches is not too complicated. It's largely based on existing numerical methods, with a focus on efficiently using those methods to not only do a forward simulation, but also to compute gradient information. What is primarily exciting in this context are the implications that arise from the combination of these numerical methods with deep learning.
 
 ## Integration
 
 Most importantly, training via differentiable physics allows us to seamlessly bring the two fields together:
-we can obtain _hybrid_ methods, that use the best numerical methods that we have at our disposal for the simulation itself, as well as for the training process. We can then use the trained model to improve the forward or backward solve. Thus, in the end we have a solver that employs both a _traditional_ solver and a _learned_ component.
+we can obtain _hybrid_ methods, that use the best numerical methods that we have at our disposal for the simulation itself, as well as for the training process. We can then use the trained model to improve forward or backward solves. Thus, in the end, we have a solver that combines a _traditional_ solver and a _learned_ component.
 
 ## Interaction
 
-One key component for these hybrids to work well is to let the NN _interact_ with the PDE solver at training time. Differentiable simulations allow a trained model to explore and experience the physical environment, and receive directed feedback regarding its interactions throughout the solver iterations. This combination nicely fits into the broader context of machine learning as _differentiable programming_. 
+One key aspect that is important for these hybrids to work well is to let the NN _interact_ with the PDE solver at training time. Differentiable simulations allow a trained model to "explore and experience" the physical environment, and receive directed feedback regarding its interactions throughout the solver iterations. This combination nicely fits into the broader context of machine learning as _differentiable programming_. 
 
 ## Generalization
 
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-Despite being a very powerful method, the DP approach is clearly not the end of the line. In the next chapters we'll consider further improvements and extensions.
+Training NNs via differentiable physics solvers, i.e., what we've described as "DP" in the previous
+sections, is a very generic approach that is applicable to a wide range of combinations of PDE-based models
+and deep learning. Nonetheless, the next chapters will discuss several variants that are orthogonal
+to the general DP version, or can yield benefits in more specialized settings.