smaller updates intro/outro

intro.md

@@ -19,7 +19,7 @@ with simulations.
 height: 220px
 name: pbdl-teaser
 ---
-Some visual examples of numerically simulated time sequences. In this book, we aim for algorithms that use neural networks alongside numerical solvers.
+Some visual examples of numerically simulated time sequences. In this book, we explain how to realize algorithms that use neural networks alongside numerical solvers.
 ```
 
 ## Coming up

outlook.md

@@ -5,7 +5,7 @@ Despite the lengthy discussions and numerous examples, we've really just barely
 
 Most importantly, the techniques that were explained in the previous chapter have an enormous potential to influence all computational methods of the next decades. As demonstrated many times in the code examples, there's no magic involved, but deep learning gives us very powerful tools to represent and approximate non-linear functions. And deep learning by no means makes existing numerical methods deprecated. Rather, the two are an ideal combination.
 
-A topic that we have not touched at all so far is, that -- of course -- in the end our goal is to improve human understanding of our world. And here the view of neural networks as "black boxes" is clearly outdated. It is simply another numerical method that humans can employ, and the physical fields predicted by a network are as interpretable as the outcome of a traditional simulation
+A topic that we have not touched at all so far is, that -- of course -- in the end our goal is to improve human understanding of our world. And here the view of neural networks as "black boxes" is clearly outdated. It is simply another numerical method that humans can employ, and the physical fields predicted by a network are as interpretable as the outcome of a traditional simulation. Nonetheless, it is important to further improve the tools for analyzing learned networks, and to extract condensed formulations of the patterns and regularities the networks have found in the solution manifolds.
 
 
 ![Divider](resources/divider2.jpg)

overview.md

@@ -15,8 +15,9 @@ height: 240px
 name: overview-pano
 ---
 Understanding our environment, and predicting how it will evolve is one of the key challenges of humankind.
-A key tool for achieving these goals are simulations, and the next generation of simulation algorithms
-will rely heavily on deep learning components to yield even more accurate predictions about our world.
+A key tool for achieving these goals are simulations, and next-gen simulations
+could strongly profit from integrating deep learning components to make even 
+more accurate predictions about our world.
 ```
 
 ## Motivation
@@ -27,31 +28,34 @@ to the control of plasma fusion {cite}`maingi2019fesreport`,
 using numerical analysis to obtain solutions for physical models has
 become an integral part of science.  
 
-At the same time, machine learning technologies and deep neural networks in particular,
+In recent years, machine learning technologies and _deep neural networks_ in particular,
 have led to impressive achievements in a variety of fields:
 from image classification {cite}`krizhevsky2012` over
 natural language processing {cite}`radford2019language`, 
 and more recently also for protein folding {cite}`alquraishi2019alphafold`.
 The field is very vibrant and quickly developing, with the promise of vast possibilities.
 
-On the other hand, the successes of deep learning (DL) approaches 
+These success stories of deep learning (DL) approaches 
 have given rise to concerns that this technology has 
-the potential to replace the traditional, simulation-driven approach to
-science. Instead of relying on models that are carefully crafted
+the potential to replace the traditional, simulation-driven approach to science. 
+E.g., recent works show that NN-based surrogate models achieve accuracies required
+for real-world, industrial applications such as airfoil flows {cite}`chen2021highacc`, while at the
+same time outperforming traditional solvers by orders of magnitude in terms of runtime.
+
+Instead of relying on models that are carefully crafted
 from first principles, can data collections of sufficient size
 be processed to provide the correct answers?
-In short: this concern is unfounded. As we'll show in the next chapters,
-it is crucial to bring together both worlds: _classical numerical techniques_
-and _deep learning_.
+As we'll show in the next chapters, this concern is unfounded. 
+Rather, it is crucial for the next generation of simulation systems
+to bridge both worlds: to 
+combine _classical numerical_ techniques with _deep learning_ methods.
 
 One central reason for the importance of this combination is
-that DL approaches are simply not yet powerful enough by themselves.
-Given the current state of the art, the clear breakthroughs of DL
-in physical applications are outstanding. 
-The proposed techniques are novel, sometimes difficult to apply, and
-significant practical difficulties combing physics and DL persist.
-Also, many fundamental theoretical questions remain unaddressed, most importantly
-regarding data efficiency and generalization.
+that DL approaches are powerful, but at the same time strongly profit
+from domain knowledge in the form of physical models.
+DL techniques and NNs are novel, sometimes difficult to apply, and
+it is admittedly often non-trivial to properly integrate our understanding
+of physical processes into the learning algorithms.
 
 Over the course of the last decades,
 highly specialized and accurate discretization schemes have
@@ -66,15 +70,15 @@ is highly beneficial for DL to use them as much as possible.
 ```{admonition} Goals of this document
 :class: tip
 The key aspects that we want to address in the following are:
-- explain how to use deep learning techniques,
+- explain how to use deep learning techniques to solve PDE problems,
 - how to combine them with **existing knowledge** of physics,
-- without **throwing away** our knowledge about numerical methods.
+- without **discarding** our knowledge about numerical methods.
 ```
 
-Thus, we want to build on all the powerful techniques that we have
+Thus, our aim is to build on all the powerful techniques that we have
 at our disposal, and use them wherever we can.
-I.e., our goal is to _reconcile_ the data-centered
-viewpoint and the physical simulation viewpoint.
+As such, a central goal of this book is to _reconcile_ the data-centered
+viewpoint with physical simulations.
 
 The resulting methods have a huge potential to improve
 what can be done with numerical methods: in scenarios

references.bib

@@ -13,6 +13,23 @@
 @STRING{NeurIPS        = "Advances in Neural Information Processing Systems"}
 
 
+@inproceedings{chen2021highacc,
+	  title={Towards high-accuracy deep learning inference of compressible turbulent flows over aerofoils},
+	  author={Chen, Li-Wei and Thuerey, Nils},
+	  booktitle={arXiv},
+	  year={2021},
+	  url={https://ge.in.tum.de/publications/},
+}
+
+@article{chen2021numerical,
+	title={Numerical investigation of minimum drag profiles in laminar flow using deep learning surrogates},
+	author={Chen, Li-Wei and Cakal, Berkay A and Hu, Xiangyu and Thuerey, Nils},
+	journal={Journal of Fluid Mechanics},
+	volume={919},
+	year={2021},
+	publisher={Cambridge University Press},
+	url={https://ge.in.tum.de/publications/2020-chen-dl-surrogates/},
+}
 
 @article{chu2021physgan,
 	author = {Chu, Mengyu and Thuerey, Nils and Seidel, Hans-Peter and Theobalt, Christian and Zayer, Rhaleb},
@@ -21,15 +38,15 @@
 	 volume = {40(4)},
 	 year = {2021},
 	 publisher = {ACM},
+     url={https://people.mpi-inf.mpg.de/~mchu/gvv-den2vel/den2vel.html},
 } 
-%  url={https://people.mpi-inf.mpg.de/~mchu/gvv-den2vel/den2vel.html},
 
 @article{franz2021globtrans,
 	 author = {Franz, Erik and Solenthaler, Barbara and Thuerey, Nils},
 	 title  ={{Global Transport for Fluid Reconstruction with Learned Self-Supervision}},
 	 journal = CVPR,
 	 year = {2021},
-	  url={https://ge.in.tum.de/publications/},
+	 url={https://ge.in.tum.de/publications/2021-franz-globtrans/},
 } 
 
 @article{um2020sol,