Combined Global and Local Search for the Falsification of Hybrid Systems

In this paper we solve the problem of finding a trajectory that shows that a given hybrid dynamical system with deterministic evolution leaves a given set of states considered to be safe. The algorithm combines local with global search for achieving both efficiency and global convergence. In local search, it exploits derivatives for efficient computation. Unlike other methods for falsification of hybrid systems with deterministic evolution, we do not restrict our search to trajectories of a certain bounded length but search for error trajectories of arbitrary length

Accelerated Molecular Dynamics for the Exascale

A range of specialized Molecular Dynamics (MD) methods have been developed in order to overcome the challenge of reaching longer timescales in systems that evolve through sequences of rare events. In this talk, we consider Parallel Trajectory Splicing (ParSplice) which works by generating large number of MD trajectory segments in parallel in such a way that they can later be assembled into a single statistically correct state-to-state trajectory, enabling parallel speedups up to N, the number of parallel workers. The prospect of strong-scaling MD is extremely enticing given the continuously increasing scale of available computational resources: on current peta-scale platforms N can be in the hundreds of thousands, which opens the door to MD-accurate millisecond-long atomistic simulations; extending such a capability into the exascale era could be transformative.In practice, however, the ability for ParSplice to scale increasingly relies on predicting where the trajectory will be found in the future. With this insight in mind, we develop a maximum likelihood transition model that is updated on the fly and make use of an uncertainty-driven estimator to approximate the optimal distribution of trajectory segments to be generated next. In addition, we investigate resource optimization schemes designed to fully utilize computational resources in order to generate the maximum expected throughput

Modelling thin film growth in the Ti-Ag system

With the aim to model the surface growth of Ti-Ag system over realistic time scales, two interatomic potential mixing rules for the Ti-Ag system were first investigated based on the embedded-atom method (EAM) elemental potentials. First principles calculations were performed using SIESTA for various configurations of the Ti-Ag system to see which model best fitted the ab initio results. The results showed that the surface energies, es- pecially that of Ti, were not well fitted by either model and the surface binding energies differed from the ab initio calculations. As a result, the modified embedded-atom method (MEAM) was investigated. In contrast to the other models, surface energies for pure Ti calculated by MEAM were in good agreement with the experimental data and the ab initio results. The MEAM mixing rule was used to investigate Ag adatoms on Ti and Ti adatoms on Ag. The results showed good agreement with SIESTA after parameter optimisation. Simulations of thin film growth in the Ag-Ti system are presented using an adaptive kinetic Monte Carlo method (AKMC). For the growth of Ti on Ag (100) and Ag (111) surfaces, the Ti adatoms prefer to exchange with the original surface layer atoms creating a mixed Ag/Ti surface. On a silver substrate, up to four mixed layers need to be formed before a pure Ti layer is obtained when the deposition energy is less than 20 eV. Conversely, the simulations of Ag on the Ti (0001) plane showed that the Ag adatoms repel each other on the Ti basal plane, before a complete first layer of Ag was obtained in a face-centred cubic structure. The implementations of a super-basin method within the adaptive ki- netic Monte Carlo method has allowed the simulation of 0.4s of surface growth on the Ag substrates. This work also compared two long time scale dynamics methods, namely AKMC and Parallel Trajectory Splicing (ParSplice) simulations. For these two configurations are considered on the Ag (111) substrate. The transitions and the associated energy barriers are identical for single atom diffusion but the diffusion rates differ. In the case of an adatom on an island, a super-basin system was created. The exit transitions found by a transition search algorithm and ParSplice were again the same whilst the mean exit time differed by a factor of two due to inaccurate prefactor calculations. The distribution of basin-exit times is also examined which obeys an exponential distribution