The reactive force-field (ReaxFF) interatomic potential is a powerful computational tool for exploring, developing and optimizing material properties. Methods based on the principles of quantum mechanics (QM), while offering valuable theoretical guidance at the electronic level, are often too computationally intense for simulations that consider the full dynamic evolution of a system. Alternatively, empirical interatomic potentials that are based on classical principles require significantly fewer computational resources, which enables simulations to better describe dynamic processes over longer timeframes and on larger scales. Such methods, however, typically require a predefined connectivity between atoms, precluding simulations that involve reactive events. The ReaxFF method was developed to help bridge this gap. Approaching the gap from the classical side, ReaxFF casts the empirical interatomic potential within a bond-order formalism, thus implicitly describing chemical bonding without expensive QM calculations. This article provides an overview of the development, application, and future directions of the ReaxFF method. INTRODUCTIONAtomistic-scale computational techniques provide a powerful means for exploring, developing and optimizing promising properties of novel materials. Simulation methods based on quantum mechanics (QM) have grown in popularity over recent decades due to the development of user-friendly software packages making QM level calculations widely accessible. Such availability has proved particularly relevant to material design, where QM frequently serves as a theoretical guide and screening tool. Unfortunately, the computational cost inherent to QM level calculations severely limits simulation scales. This limitation often excludes QM methods from considering the dynamic evolution of a system, thus hampering our theoretical understanding of key factors affecting the overall behaviour of a material. To alleviate this issue, QM structure and energy data are used to train empirical force fields that require significantly fewer computational resources, thereby enabling simulations to better describe dynamic processes. Such empirical methods, including reactive force-field (ReaxFF), 1 trade accuracy for lower computational expense, making it possible to reach simulation scales that are orders of magnitude beyond what is tractable for QM.Atomistic force-field methods utilise empirically determined interatomic potentials to calculate system energy as a function of atomic positions. Classical approximations are well suited for nonreactive interactions, such as angle-strain represented by harmonic potentials, dispersion represented by van der Waals potentials and Coulombic interactions represented by various polarisation schemes. However, such descriptions are inadequate for modelling changes in atom connectivity (i.e., for modelling chemical reactions as bonds break and form). This motivates the

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First order methods, which solely rely on gradient information, are commonly used in diverse machine learning (ML) and data analysis (DA) applications. This is attributed to the simplicity of their implementations, as well as low per-iteration computational/storage costs. However, they suffer from significant disadvantages; most notably, their performance degrades with increasing problem ill-conditioning. Furthermore, they often involve a large number of hyper-parameters, and are notoriously sensitive to parameters such as the step-size. By incorporating additional information from the Hessian, second-order methods, have been shown to be resilient to many such adversarial effects. However, these advantages of using curvature information come at the cost of higher per-iteration costs, which in "big data" regimes, can be computationally prohibitive.In this paper, we show that, contrary to conventional belief, second-order methods, when implemented appropriately, can be more efficient than first-order alternatives in many largescale ML/ DA applications. In particular, in convex settings, we consider variants of classical Newton's method in which the Hessian and/or the gradient are randomly sub-sampled. We show that by effectively leveraging the power of GPUs, such randomized Newton-type algorithms can be significantly accelerated, and can easily outperform state of the art implementations of existing techniques in popular ML/ DA software packages such as TensorFlow. Additionally these randomized methods incur a small memory overhead compared to first-order methods. In particular, we show that for million-dimensional problems, our GPU accelerated sub-sampled Newton's method achieves a higher test accuracy in milliseconds as compared with tens of seconds for first order alternatives.