I am taking a Thesis-based Master degree now and I am going to choose my supervisor soon. I plan to take a PHD degree after graduation, so if possible, I wish my PHD research area could be an extension of my Master Thesis ( so that the researching experience during my Master wouldn't be wasted).

Currently I am interested in the research areas of two professors. Professor A focuses on Numerical Solution on PDE. Professor B conducted research on Numerical PDE several years ago (He was the supervisor of Professor A's Master Thesis) but it seems that he has changed his research field to Inverse Problems in the last 5 years.

Because I am not quite familiar with Inverse Problem, currently I am more interested in Numerical PDE. But since Professor B has richer researching experience, I think his recommendation may be more helpful for my PHD application.

So may I ask what is the basic knowledge for research on Inverse Problem? Does it share the same research technique with researching on Numerical PDE? Is it possible for me to change from Numerical PDE to Inverse Problem without encountering many difficulties ( in PHD application and researching)?

Thanks for your help. Any comment would be highly appreciated.

  • $\begingroup$ Welcome to SciComp. You may consider leaving out the background and reducing your question to the essence. $\endgroup$ – Jan Nov 5 '13 at 7:35

If you plan to continue your PhD with the same adviser at the same university, then it seems to me your plan to keep the topics related is a good one. But, since it sounds like you want to do your Masters degree and then find a new (better?) place with a new adviser, I'd suggest that you're likely to find it hard to keep the exact topic going.

This doesn't mean that your Masters degree research will have been wasted, though! If you plan carefully, the background you develop while working on your Masters degree will dovetail nicely with your PhD topic. One prepares you for the other.

You've given a good example in your question, in fact. Numerical solution of PDEs is a part of the numerical solution of inverse problems. You can't to do the latter without the former. You could do a Masters with the PDE adviser and then move on to a PhD in inverse problems if that was interesting to you.

| cite | improve this answer | |
  • $\begingroup$ Thanks for your kind sharing! Yes, you are right. I plan to strengthen my research ability during Master and pursuit my PHD in a better university. From your reply, it seems Numerical PDE is more fundamental or theoratical than Inverse problem. That 's why you say I can change field from Numerical PDE to Inverse Problem. But how about the converse, is it possible for me to move to Numerical PDE from Inverse Problem? $\endgroup$ – John Nov 5 '13 at 15:58
  • $\begingroup$ That was just an example, but you probably can't do Inverse Problems related to PDE forward problems without some ability to solve the PDEs numerically. You're probably going to have to learn a lot about numerical solution of PDEs to do inverse problems for PDEs. I'm not telling you what to do with your life, but if your ultimate goal is to solve inverse problems, you're going to have to go through numerical solution to PDEs to get there. $\endgroup$ – Bill Barth Nov 5 '13 at 19:44

Forward modeling alone is of little use. 'Most' problems, both in engineering and science are really inverse problems. No matter how cool you forward models are unless you can use it to optimize something or estimate some parameters of interest (that have scientific implications) it will be of little use in applied sciences. So yes PDE constrained optimization is a good area.

However you also need to learn how to solve forward models (numerically I presume) and it does require some basic skills. So you can do you MS in numerical solution of PDE's (hopefully write a code) and then later pursue a PhD in inverse problems (and apply your code) to solve interesting problems and publish papers.

It is natural for people who do forward modeling to move into inverse modeling later on and it might very well be that Prof A follows the steps taken by Prof B. In fact there are many such examples, specially in the HPC community. A few decades back computers weren't powerful enough to solve forward problems, let alone inverse problems but now solution of inverse problems is routine, both in academia and industry.

| cite | improve this answer | |
  • 2
    $\begingroup$ I think your whole comment is more than a little excessive. The development of new PDE simulation techniques is stil, IMO, an important area of research. Most PDEs are in no way optimally solvable. $\endgroup$ – Bill Barth Nov 5 '13 at 14:02
  • $\begingroup$ It all depends on your area. Theoreticians come up with new methods/schemes and applied folks use it to solve problems. IMHO, it is very difficult to come up with a new method (e.g., XFEM) than to use it to do science. $\endgroup$ – stali Nov 5 '13 at 14:08

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.