computational methods for statistical mechanics [day #4]

My last day at this ICMS workshop on molecular simulation started [with a double loop of Arthur’s Seat thankfully avoiding the heavy rains of the previous night and then] Chris Chipot‘s magistral entry to molecular simulation for proteins with impressive slides and simulation movies, even though I could not follow the details to really understand the simulation challenges therein, just catching a few connections with earlier talks. A typical example of a cross-disciplinary gap, where the other discipline always seems to be stressing the ‘wrong” aspects. Although this is perfectly unrealistic, it would immensely to prepare talks in pairs for such interdisciplinary workshops! Then Gersende Fort presented results about convergence and efficiency for the Wang-Landau algorithm. The idea is to find the optimal rate for updating the weights of the elements of the partition towards reaching the flat histogram in minimal time. Showing massive gains on toy examples. The next talk went back to molecular biology with Jérôme Hénin‘s presentation on improved adaptive biased sampling. With an exciting notion of orthogonality aiming at finding the slowest directions in the target and putting the computational effort. He also discussed the tension between long single simulations and short repeated ones, echoing a long-going debate in the MCMC community. (He also had a slide with a picture of my first 1983 Apple IIe computer!) Then Antonietta Mira gave a broad perspective on delayed rejection and zero variance estimates. With impressive variance reductions (although some physicists then asked for reduction of order 10¹⁰!). Johannes Zimmer gave a beautiful maths talk on the connection between particle and diffusion limits (PDEs) and Wasserstein geometry and large deviations. (I did not get most of the talk, but it was nonetheless beautiful!) Bert Kappen concluded the day (and the workshop for me) by a nice introduction to control theory. Making connection between optimal control and optimal importance sampling. Which made me idly think of the following problem: what if control cannot be completely… controlled and hence involves a stochastic part? Presumably of little interest as the control would then be on the parameters of the distribution of the control.

“The alanine dipeptide is the fruit fly of molecular simulation.”

The example of this alanine dipeptide molecule was so recurrent during the talks that it justified the above quote by Michael Allen. Not that I am more proficient in the point of studying this protein or using it as a benchmark. Or in identifying the specifics of the challenges of molecular dynamics simulation. Not a criticism of the ICMS workshop obviously, but rather of my congenital difficulty with continuous time processes!!! So I do not return from Edinburgh with a new research collaborative project in molecular dynamics (if with more traditional prospects), albeit with the perception that a minimal effort could bring me to breach the vocabulary barrier. And maybe consider ABC ventures in those (new) domains. (Although I fear my talk on ABC did not impact most of the audience!)