Would it be professional to ask my host to cover my dining and commuting expenses? I'm a M.Sc student in europe who is collaborating with a prof on a research project. He works in an institute which is in a different city than mine. He has offered to cover my up and down weekely train tickets.

Though the train trip in one direction is just 3 hours. Its during the lunch and dinner times when I'm on the train and the meals on the train are not included on the ticket and quite expensive for a weekly affair. For now, I pack some snacks with me but its by no means a full satisfactory meal. Essentially I starve for the whole day with no eating options at the host institute. Moreover, I travel for 45 mins by public transport one way from the station to the institute (i'm not sure if I can ask for taxi expenses either)

The meetings are for discussions on progress, ideas and general presentations on relevant papers. Its been very useful but I don't want to extend his generosity beyond the point where it becomes unprofessional.

I wish to keep this collaboration between me and him as professional as possible. Since I have no prior experience of a professor inviting me for discussing and working towards a common goal, I fail to find the line between ethical and unethical expenses which I can ask the supervisor for.

Any suggestions are appreciated! Thanks
I've only been a visitor in the European context, but I believe these costs would be reasonable to bring up. (First check whether there are funds at your institution that could help cover the difference. Ask your advisor and perhaps a department administrator for ideas.) Below is a possible script and some potential ways to save money.


  I'm getting a lot out of these weekly meetings, and I appreciate your making this possible by funding my train tickets, but I have been surprised by several aspects of the cost of travel that I did not initially expect. Finding food during the trip, and getting to the train station in an efficient way are actually adding up. Unfortunately, my institution does not have funds that will cover this. Is there any way your research funds could cover this as well? Or can we rearrange our meetings to cut costs?


Travel: 


Now that you have communicated a lot in person, could you switch to an online meeting every other week? If there are regulations that say he can only cover train fare, at least you would cut your other expenses in half. Or he may be able to pay for a taxi and food with the savings from the train fares.
If your schedule remains regular, could you find other regular commuters to split the cost of a taxi and/or to reimburse for being a passenger in their car? Your institution may have a bulletin board, or there may be ride sharing services in your area that help with this.
Is there a regular taxi driver who may be able to coordinate with you? If you're able to regularly ride with someone at the beginning or end of their shift, for instance, they might appreciate that consistency and offer a discount.  


Food:


You could ask if there is any way to buy or order food while you are at the institute; it may be cheaper than on the train, and he may decide to pay for your food when you visit.
My department does reimburse for food eaten away from home as part of travel, but I might personally find this harder to bring up.
You may also be able to get several sandwiches or pre-made meals for the trip, or get cheaper food at the train station itself.


Time:


You're probably exhausted after each one of these trips, and that feeling can add up. This might be another reason to change the schedule, perhaps spending a few days there at once, but not visiting as often. (Does the institute have guest housing, and/or is there a hostel nearby?)
Taking public transport to cut costs could work occasionally, but your time on transportation alone is going to be 7.5 hours, not to mention time waiting and transferring. It is reasonable to feel like that is not sustainable.