How not to lose confidence in front of supervisor? I have been working on my doctoral thesis with a very well known professor in the field. I am going to finish 1 year of my study with him. As usual, we have been meeting every week at least once on the problem.

Problem: No matter how much I do prepare about the possible discussion on any topic, I have been losing confidence in front of him almost in every discussion. This is probably has something to do with me thinking that I am not capable of working with him. My standard is not that much. I don't know whether is this normal? How do I get over this problem? Sometimes, I can't even speak properly when he sends me to the whiteboard for any explanation. This is weird. I feel really bad after that. I keep messing up discussions. However, he gives me time. Can I get a few suggestion on this?

Note: English, which is not my native language, is the language of communication during these discussions.
I experienced something similar at the beginning of my PhD. It was mostly due to the fact that as I was verbalising my ideas, I'd realise their flaws, that they don't quite make sense, or that I hadn't it as figured out as I thought.

I suggest you try to verbally explain your ideas to someone else (if no one else, plushies are great listeners) before you talk to him, that'll give you extra confidence. It is important that you speak out loud, and from the beginning: don't skip right to the meat of the question, your problem may be in the fundamentals.

If this is your problem, once you get the hang of it, you'll quickly learn how to weed out some of these bad ideas, and gain confidence on your explanations.

Something I have seen my students struggle with (and probably myself too, but I don't notice it so much) is that when I ask them a question, they try to answer it as soon as possible, so they get stuck in suboptimal explanations, increase their confusion, get more stressed, and lastly blocked. He is giving you time, so take it, think carefully about what you are going to say, and explore different ways of expressing it before you start saying it. And furthermore, if you find a better way of explaining it, feel free to scratch what you just said and start all over again.

Another option is to set the the ground for a discussion by sending a long email taking your time to explain everything. And if you feel you didn't manage to get your point across, never hesitate to send it after the fact.

Lastly, for a few weeks I got the feeling that my supervisor wasn't really understanding what I am trying to do; but after I gave a 30 min presentation of my work in the department, from the bottom up, he got very excited, and now his comments are, I feel, much more spot on. The presentation included explaining my tools for people completely unfamiliar with them (to be specific, a specific technique built on deep learning for machine [but not deep] learning practitioners).

For your case, consider asking for some time, thinking on it on your own, and coming back with an explanation whenever you have it.