FEREBUS: Highly parallelized engine for kriging training

Abstract

[a] FFLUX is a novel force field based on quantum topological atoms, combining multipolar electrostatics with IQA intraatomic and interatomic energy terms. The program FEREBUS calculates the hyperparameters of models produced by the machine learning method kriging. Calculation of kriging hyperparameters (h and p) requires the optimization of the concentrated loglikelihoodLðh; pÞ. FEREBUS uses Particle Swarm Optimization (PSO) and Differential Evolution (DE) algorithms to find the maximum ofLðh; pÞ. PSO and DE are two heuristic algorithms that each use a set of particles or vectors to explore the space in whichLðh; pÞ is defined, searching for the maximum. The loglikelihood is a computationally expensive function, which needs to be calculated several times during each optimization iteration. The cost scales quickly with the problem dimension and speed becomes critical in model generation. We present the strategy used to parallelize FEREBUS, and the optimization ofLð h; pÞ through PSO and DE. The code is parallelized in two ways. MPI parallelization distributes the particles or vectors among the different processes, whereas the OpenMP implementation takes care of the calculation ofLðh; pÞ, which involves the calculation and inversion of a particular matrix, whose size increases quickly with the dimension of the problem. The run time shows a speed-up of 61 times going from single core to 90 cores with a saving, in one case, of 98% of the single core time. In fact, the parallelization scheme presented reduces computational time from 2871 s for a single core calculation, to 41 s for 90 cores calculation.

Contributions of IQA electron correlation in understanding the chemical bond and non-covalent interactions

“…Three different types of ML techniques, that is, Random Forest (RF), Support Vector Regression (SVR), and Kriging [39,56,[66][67][68][69], were applied to predict correlation energies of three systems: the water monomer, the H 2 -He complex and the water dimer. In the first system, intramolecular-interatomic correlation energies were investigated, while in the last two, the intermolecular correlation energies are in the spotlight, since they are correlated with intermolecular dispersion forces.…”

Towards the simulation of biomolecules: optimisation of peptide-capped glycine using FFLUX

“…Secondly, 1000 of the remaining conformations were chosen at random and used to build the training set. The in-house program FEREBUS [53] was used to build the Kriging where R n ALF is the position vector of atom n in the ALF of Ω and n i (i = 1, 2, 3) is a Cartesian coordinate expressed in the ALF. The full account of the above and the derivation of the analytical forces is intricate and given in great detail in previous work by Mills and Popelier [42].…”

“…The values of the Kriging parameters A h are optimised using particle swarm optimisation to maximise the concentrated log-likelihood. Particle Swarm Optimisation as used in FEREBUS has been described fully by Di Pasquale et al [53].…”

The accuracy of ab initio calculations without ab initio calculations for charged systems: Kriging predictions of atomistic properties for ions in aqueous solutions

“…Note that we adhere to the standard IQA notation of Vcl, where the subscript refers to "classical" and of course not to chlorine. From here, each configuration (input) and its corresponding energies (output) are used as training points for our kriging program FEREBUS 29,30 . This program calculates the so-called hyperparameters θ and p of the models, as shown in Eq.…”