How do I correctly abbreviate compounded first name for academic publications?

The most important thing is consistency. Choose now, and write the exact same name on all future publications.

A few things to consider:

• This is the name that everyone, except the people that know you personally, will use. So make sure you are not going to regret it.
• It is better to choose a name that identifies you as well as possible. If your first and last names are very common, it may be beneficial to add the second part of your given name, or your middle name, so that people are sure who wrote the paper just by looking at the name. If your name is already uncommon, this is a less pressing concern.
• Many people, especially in North America as I have found, are completely unfamiliar with the idea of compound names. Somehow, even generally open-minded people are reluctant (I do not use this word light, if I wanted to write "surprised" or "unfamiliar" that's what I would have written!) to accept that a name might not fit their traditional "GivenName MiddleName Surname" mental framework and will try to fit your name into their expectations, not the other way around, even after you have explained it to them. It is really frustrating and invalidating, but be prepared.
• Computer systems are also a beast to be prepared to fight. The big international ones are almost always written with North American expectations in mind.
• If you decide to use both parts of your given name, I strongly recommend joining the two with a dash, even if that is not culturally appropriate for you and/or does not match your ID card. This makes things a lot easier as it is clearer that these two parts are linked and cannot be taken apart. My surname is from a language where dashes do not even exist, and until I decided to use a dash I had to face incomprehension, even from people to whom I had carefully explained what's what.

For your particular case, if you are willing to be called "FirstName M[iddleNameInitial]. LastName", that sounds perfectly fine. Dropping the second part of your compound given name is fine if you are okay being called with just the first part, in emails or daily conversations. There is no requirements, legal or otherwise, that your legal name must match the name on your publications.