Hi Bruno,
We are currently working on our DEM simulation engine using deal.II particles
features. DEM lead to very chaotic systems (with positive Lyapunov exponents,
like in MD), which means that slight discrepancies in floating point numbers
can lead to exponentially different results. You can imagine for example that
if a particle is to fall exactly on top of another, a slight difference in
round-off error can lead to the particle sliding to the right or to the left
of the other particle. Consequently, very small differences accumulate and
lead to drastically different results.
Right now, we are testing everything using numdiff within a ctest framework
identical to deal.II. However, since we are comparing text files with
particles positions and velocities, the tests end up being extremely fragile
because they depend on the compiler version and MPI library being used (I guess?).
I was wondering if any of you had experience on what would be the best way to
write functional tests that test the full code in the context of systems which
show highly chaotic behavior like this? Right now we try to test for very
small time, thus ensuring that differences don't have the time to propagate,
but this is becoming more and more fragile and sometimes tests will crash on a
peculiar machine, yet work on 95% of the other ones (such as our github actions).
Interesting :-)
I think that conceptually, you probably do want to test certain aspects of
your code in this deterministic way. For example, if you want to check the
correctness of the particle trajectory integrator, you can do that with a
small number of particles whose trajectories stay well away from chaotic points.
But there are of course also other aspects that really are chaotic and that
you also want to test. In those cases, you need to identify the statistical
properties that *do* behave deterministically. For example, the motion of
individual stars in globular star clusters is likely chaotic, but the motion
of the center of mass, or the evolution of the angular momentum and total
energy is not. These are things you can compute and output and they should be
comparable among compilers and platforms. If you have enough particles, you
could also consider things such as kernel density estimates of particle
densities, momentum densities, etc.
Best
W.
--
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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