Me and my advisor have weekly meetings. But this week, I didn't have much progress so we won't have much to discuss. I want to cancel the meeting. How to gracefully express that "I don't have much progress this week" without giving him/her the impression that "I didn't work much"(which is true)?
I have been in your exact situation many, many times.
More often than not, my temptation (and often what I do) is to send an email a day in advance like "I haven't made much progress since last week. I would be happy to meet if you have something you would like to discuss, but I am also happy to use the time to continue making progress on what we discussed last week." So long as this doesn't happen several times in a row, it is almost always fine, and your supervisor is also busy and I'm sure can other find things to fill one hour.
However, sometimes I (ironically) put off sending that email and the meeting happens anyway, or sometimes the professor wants to meet despite my protests. Sometimes this goes the way you expect -- there's a short meeting that basically ends with "ok let's check in again in a week." However more often than not, and always to my surprise, these meetings can become very interesting sessions where we talk about the project at a higher level without getting bogged down in the week-to-week details. Some very interesting ideas have come out of this, often things that I would never have even thought to try, or new research directions for the project.
So... I'm not sure there is good general advice. If you are clear on what you want to work on, then sending an email to postpone is probably fine and if anything appreciated. But I think it's also ok to keep the meeting and go in with an open mind.
ps -- in the case where you don't make progress for several weeks in a row, the solution isn't to be ashamed that you haven't made progress, but to take stock and ask where you are stuck. Sometimes bringing a clear description of a roadblock to a research meeting is just as valuable as bringing tangible progress, since it may point to a problem that needs to be solved that your advisor didn't expect. Often these periods can be associated with feelings of shame and imposter syndrome and low motivation, but that doesn't mean you are actually doing poorly. Sometimes finding a way around your problem or a way to simplify the problem into something more manageable, rather than stick to the original plan, actually is the best thing you can do.
In a field like mine (math or cs) it is perfectly natural for research to proceed at an uneven pace. I suspect that is true in many fields.
I'd guess your advisor won't be too surprised if you tell them. But you can just ask if they think a meeting is needed and whether there might be things to discuss and ideas to pursue.
And, "not working" for a week is also not that uncommon since our mental energy levels rise and fall and life often intrudes. Whether you want to say that you didn't work is up to you, unless there is some reason for it.
But, if you always made progress at a steady rate there would be little need for meetings anyway. This might be the most important time to have one. And, "proceeding at a steady rate" doesn't really describe research very well.
But phrasing it as a question (should we meet) is probably better than the alternative.
I think this week is particularly more important for you to meet your advisor. I would suggest you meet with your advisor and discuss with him the reason why you were not able to make much progress. Was it because of the nature of question you're working on? Is the question/solution not clear to you? Was it because of lack of prerequisites? In which case he could suggest you some reading. Were you not able to make much progress because of personal reasons? For e.g. stress, depression, lack of motivation, etc. Then, he might suggest some other resources or maybe even motivate you in a manner which might again spark your interest in the subject; because sometimes it takes some experience to see how interesting a particular topic is.
I don't think he would have any bad impression about you or judge you if you tell him the truth.
A (research) meeting does not have to be just about reporting progress. It can be about bringing everyone involved up to date about the status of activities relevant to the success of the (research) project.
Create a summary template with this view in mind.
- Report of New Discoveries
Example: Report on literature that you read that impacts the direction of the research.
- Report on Status of Unresolved Activities from Previous Meeting
Example: Itemize top-level actions that were set at the last meeting and state whether they are completed, ongoing, on hold, or delegated/delayed (waiting on). Provide background information as needed to resolve how to move any uncompleted actions forward for the next meeting.
- Proposals for New Activities
Example: Suggest an upcoming conference that you want to attend or a new theoretical approach that you would like to learn more about.
Finally, plan to use the end of the meeting to create/review a list of actions that you and the other team members should report on at the next meeting.
In summary, you do not have to be embarrassed that you will meet and will report no progress. Stuff happens, delays occur, and yet effective teams still meet to discuss their collaborative project. The greatest benefit will be when you can effectively summarize how the inadvertent delay may impact your timeline to meet your goals, how you might plan to make up the delay going forward, or where you feel you need help to overcome unanticipated problems in your work.