Are you serious.. SAT solvers have some of the hardest code I have seen. Look at the SAT solvers that won satcompetition. On the other hand IMO, implementing a neural network on your own is very easy. But the point is not that. I consider the neural network libraries(e.g. tensorflow) as given, as it is in not related to the problem, and can be used in many different problems. I will consider only the code above the neural network API for the complexity(like models, encoding etc.). But a SAT solver has a specific function and is core part of the problems it is trying to solve.

I think you are running afoul of not realizing that "world class" neural networks are a ton of code. Just as a trivial SAT solver is easy and can be implemented rather quickly.

Now, neither will be that good at the job they are made for. But that is far from unique to this field. Consider, a car/bike/house/whatever is not exactly hard to build for backyard use. Getting world class, on the other hand, escalates to difficult very quickly.

Yes, competitive SAT solvers are very complicated. However, they are not outside of most developers' abilities. During a verification course at my University we had to build a simple SAT solver. Most students were able to complete the project in ~20-30 hours. Mine wasn't fast, but it worked well enough to be a proof of concept.

Also, saying that NN are easy with a library like tensorflow is akin to saying that Sudoku solvers are easy with Prolog. Of course they are! The library/language does the vast majority of the heavy lifting.

There are super-complicated SAT solvers certainly, but MiniSAT has (in my opinion) reasonably easy to understand code. It's not very long either. Have you tried reading the code to Tensorflow?

Also, in my personal experience, SAT is currently applicable to more problems than Neural Networks (although that is changing as Neural Networks get applied to more things). You can use SAT solvers to solve any problem in NP (well, other things as well but it rapidly gets painful). That's a lot of problems!

I just want to mention that this NN code is as simple as it gets and that anyone remotely knowing what they're doing could code op's thing in about 2 hrs.