The atomic simulation environment (ASE) is a software package written in the Python programming language with the aim of setting up, steering, and analyzing atomistic simulations. In ASE, tasks are fully scripted in Python. The powerful syntax of Python combined with the NumPy array library make it possible to perform very complex simulation tasks. For example, a sequence of calculations may be performed with the use of a simple 'for-loop' construction. Calculations of energy, forces, stresses and other quantities are performed through interfaces to many external electronic structure codes or force fields using a uniform interface. On top of this calculator interface, ASE provides modules for performing many standard simulation tasks such as structure optimization, molecular dynamics, handling of constraints and performing nudged elastic band calculations.

Statistical learning based on a local representation of atomic structures provides a universal model of chemical stability.

We present a molecular dynamics scheme which combines first-principles and machine-learning (ML) techniques in a single information-efficient approach. Forces on atoms are either predicted by Bayesian inference or, if necessary, computed by on-the-fly quantum-mechanical (QM) calculations and added to a growing ML database, whose completeness is, thus, never required. As a result, the scheme is accurate and general, while progressively fewer QM calls are needed when a new chemical process is encountered for the second and subsequent times, as demonstrated by tests on crystalline and molten silicon. [18] to fit "once and for all" the DFT potential energy surface (PES), after which atomic forces are obtained by analytic differentiation. Similar to classical FFs, a fixed highquality parametrized PES simultaneously ensures fast force evaluation and reliable interpolation. However, accuracy is still not guaranteed to transfer to chemical situations not represented in the fitting database.Here, we propose an alternative machine-learning (ML) based scheme where we allow a stream of fresh quantummechanical (QM) calculations to augment the ML database during each MD simulation, enabling safe interpolation. The scheme could equally be viewed as an efficient FPMD approach where we seek to compute only the QM information necessary to progress the simulation, while retaining the very broad applicability of FPMD. To minimize the QM workload of the MD simulation, one can start by noticing that ML-predicted atomic forces will suffice as long as the dynamics visits configuration is "well represented" within the existing database. Thus, an ideal ML MD scheme should not attempt to increase its database through additional QM calculations until "something new" happens that necessitates this. This is a central guideline for the present work, significantly improving on an earlier scheme [19,20] where all QM information was used once and afterwards discarded. Our new scheme has the potential to reduce the cost of FPMD for the vast range of problems where it is already applied [2], and to extend its use to problems currently beyond reach because of prohibitive time and/or length scales. Here, we test it on standard benchmark physical systems [3,17,18,20], comprising crystalline and molten silicon over a wide range of temperatures and bonding geometries, in both insulating and metallic conditions (Figs. 1-3). FIG. 1 (color online).Comparison of the bulk Si phonon spectrum calculated with DFTB (blue), and SW (black) and with the ML on-the-fly (MLOTF) approach (red), computed with the finite displacement Parlinksi-Li-Kawazoe method [21,22] using a standard σ err ¼ 0.05 eV=Å (dotted lines) and a highaccuracy σ err ¼ 5 × 10 −4 eV=Å value (solid lines) for the ML data noise parameter. The ML database was constructed from a 300 K MD trajectory.

The success of first principles electronic structure calculation for predictive modeling in chemistry, solid state physics, and materials science is constrained by the limitations on simulated length and time scales due to computational cost and its scaling. Techniques based on machine learning ideas for interpolating the Born-Oppenheimer potential energy surface without explicitly describing electrons have recently shown great promise, but accurately and efficiently fitting the physically relevant space of configurations has remained a challenging goal. Here we present a Gaussian Approximation Potential for silicon that achieves this milestone, accurately reproducing density functional theory reference results for a wide range of observable properties, including crystal, liquid, and amorphous bulk phases, as well as point, line, and plane defects. We demonstrate that this new potential enables calculations that would be very expensive with a first principles electronic structure method, such as finite temperature phase boundary lines, self-diffusivity in the liquid, formation of the amorphous by slow quench, and dynamic brittle fracture. We show that the uncertainty quantification inherent to the Gaussian process regression framework gives a qualitative estimate of the potential's accuracy for a given atomic configuration. The success of this model shows that it is indeed possible to create a useful machine-learning-based interatomic potential that comprehensively describes a material, and serves as a template for the development of such models in the future.