Hello Axel,
Thank you for your very helpful response. I have thought about the Lyapunov
exponents that you mention here, and also about the shadowing theorem. As
you said, the uncertainties in MD are mostly related to energy and the
interatomic potential.
no, they are not and that is not what i was saying. the uncertainties
are typically dominated by incomplete statistical sampling, finite
size effects and approximations to the nature of the interactions
(e.g. reducing manybody interactions to pairwise additive interactions
and thus relying to a very large degree on error cancellation). again,
this is explained in texts on statistical mechanics, which is the
theory that connects the mircoscopic properties computed in MD
simulations to bulk (thermodynamic) properties.
So in this study, I'm taking into account that many
potentials are calibrated against some known, but different quantities (e.g.
Young moduli, stacking fault energy, etc.) and thus create numerous
potentials for the same element. The approach that I'm using is the optimal
interval approach (which is an intrusive UQ method) and I hope somehow I can
get lammps adapt to it.
but that would this tell you, that cannot be better be evaluated by a
simple sensitivity analysis (i.e. repeat the computation of such
properties with a series of different parameter sets and then measure
the response of the desired property to those changes)? please keep in
mind that typically such calibration properties are not simple static
properties that are determined from a single energy evaluation, but
require sufficient statistical sampling to achieve a converged
property. it is a bit different for properties that are determined
from a series of energy minimizations, but those are not strictly
molecular *dynamics* calculations, since those are properties computed
at 0K temperature.
Please allow me to rephrase my question: is it possible to modify lammps
somehow to adapt to the interval formulation instead of real number
formulation, assuming the ensemble are also reformulated in interval as
well. That would be great if so.
that is not really a reformulation of the question but a restatement
and i already answered that with a "no". you would have to rewrite
practically all of the code. as i mentioned, it would be easier to
write a new MD code from scratch. a simple serial MD code for a single
type of atoms with a simple LJ potential and no thermostat is fairly
easy to implement. a complex code like LAMMPS requires a *massive*
amount of programming, including all the parallel communication and
many other complex tasks, not to mention the amount of debugging
required and the performance hit inferred.
but writing your own code would not make your prospects of producing
any meaningful information any better in my opinion.
axel.