Getting better

One of our main tools in our research are numerical simulations. E.g. the research of the previous entry would have been impossible without.

Numerical simulations require computers to run them. And even though computers become continuously more powerful, they are limited in the end. Not to mention that they cost money to buy and to use. Yes, also using them is expensive. Think of the electricity bill or even having space available for them.

So, to reduce the costs, we need to use them efficiently. That is good for us, because we can do more research in the same time. And that means that we as a society can make scientific progress faster. But it also reduces financial costs, which in fundamental research almost always means the taxpayer's money. And it reduces the environmental stress which we exercise by having and running the computers. That is also something which should not be forgotten.

So what does efficiently mean?

Well, we need to write our own computer programs. What we do nobody did before us. Most of what we do is really the edge of what we understand. So nobody was here before us and could have provided us with computer programs. We do them ourselves.

For that to be efficient, we need three important ingredients.

The first seems to be quite obvious. The programs should be correct before we use them to make a large scale computation. It would be very wasteful to run on a hundred computers for several months, just to figure out it was all for naught, because there was an error. Of course, we need to test them somewhere, but this can be done with much less effort. But this takes actually quite some time. And is very annoying. But it needs to be done.

The next two issues seems to be the same, but are actually subtly different. We need to have fast and optimized algorithms. The important difference is: The quality of the algorithm decides how fast it can be in principle. The actual optimization decides to which extent it uses this potential.

The latter point is something which requires a substantial amount of experience with programming. It is not something which can be learned theoretically. And it is more of a craftsmanship than anything else. Being good in optimization can make a program a thousand times faster. So, this is one reason why we try to teach students programming early, so that they can acquire the necessary experience before they enter research in their thesis work. Though there is still today research work which can be done without computers, it has become markedly less over the decades. It will never completely vanish, though. But it may well become a comparatively small fraction.

But whatever optimization can do, it can do only so much without good algorithms. And now we enter the main topic of this entry.

It is not only the code which we develop by ourselves. It is also the algorithms. Because again, they are new. Nobody did this before. So it is also up to us to make them efficient. But to really write a good algorithm requires knowledge about its background. This is called domain-specific knowledge. Knowing the scientific background. One reason more why you cannot get it off-the-shelf. Thus, if you want to calculate something new in research using computer simulations that means usually sitting down and writing a new algorithm.

But even once an algorithm is written down this does not mean that it is necessarily already the fastest possible one. Also this requires on the one hand experience, but even more so it is something new. And it is thus research as well to make it fast. So they can, and need to be, made better.

Right now I am supervising two bachelor theses where exactly this is done. The algorithms are indeed directly those which are involved with the research mentioned in the beginning. While both are working on the same algorithm, they do it with quite different emphasis.

The aim in one project is to make the algorithm faster, without changing its results. It is a classical case of improving an algorithm. If successful, it will make it possible to push the boundaries of what projects can be done. Thus, it makes computer simulations more efficient, and thus satisfies allows to do more research. One goal reached. Unfortunately the 'if' already tells that, as always with research, there is never a guarantee that it is possible. But if this kind of research should continue, it is necessary. The only alternative is waiting for a decade for the computers to become faster, and doing something different in the time in between. Not a very interesting option.

The other one is a little bit different. Here, the algorithm should be modified to serve a slightly different goal. It is not a fundamentally different goal, but subtly different so. Thus, while it does not create a fundamentally new algorithm, it still does create something new. Something, which will make a different kind of research possible. Without the modification, the other kind of research may not be possible for some time to come. But just as it is not possible to guarantee that an algorithm can be made more efficient, it is also not always possible that an algorithm with any reasonable amount of potential can be created at all. So this is also true research.

Thus, it remains exciting of what both theses will ultimately lead to.

So, as you see, behind the scenes research is quite full of the small things which make the big things possible. Both of these projects are probably closer to our everyday work than most of the things I have been posting before. The everyday work in research is quite often grinding. But, as always, this is what makes the big things ultimately possible. Without such projects as these two theses, our progress would be slowed down to a snail's speed.