I am curious as to how F# performance compares to C++ performance? I asked a similar question with regards to Java, and the impression I got was that Java is not suitable f
In addition to what others said, there is one important point about F# and that's parallelism. The performance of ordinary F# code is determined by CLR, although you may be able to use LAPACK from F# or you may be able to make native calls using C++/CLI as part of your project.
However, well-designed functional programs tend to be much easier to parallelize, which means that you can easily gain performance by using multi-core CPUs, which are definitely available to you if you're doing some scientific computing. Here are a couple of relevant links:
Regarding distributed computing, you can use any distributed computing framework that's available for the .NET platform. There is a MPI.NET project, which works well with F#, but you may be also able to use DryadLINQ, which is a MSR project.