Adaptive machine learning framework to accelerate ab initio molecular dynamics

Abstract

Quantum mechanics-based ab initio molecular dynamics (MD) simulation schemes offer an accurate and direct means to monitor the time evolution of materials. Nevertheless, the expensive and repetitive energy and force computations required in such simulations lead to significant bottlenecks. Here, we lay the foundations for an accelerated ab initio MD approach integrated with a machine learning framework. The proposed algorithm learns from previously visited configurations in a continuous and adaptive manner on-the-fly, and predicts (with chemical accuracy) the energies and atomic forces of a new configuration at a minuscule fraction of the time taken by conventional ab initio methods. Key elements of this new accelerated ab initio MD paradigm include representa-tions of atomic configurations by numerical fingerprints, a learning algorithm to map the fingerprints to the properties, a decision engine that guides the choice of the prediction scheme, and requisite amount of ab initio data. The performance of each aspect of the proposed scheme is critically evaluated for Al in several different chemical environments. This work has enormous implications beyond ab initio MD acceleration. It can also lead to accelerated structure and property prediction schemes, and accurate force fields.

Communication: Understanding molecular representations in machine learning: The role of uniqueness and target similarity

“…In practice, addressing the former drawback is less important since one typically knows beforehand which ranges of interatomic distances and chemical compositions are relevant to the chemical problem at hand: It is straightforward to define the appropriate domain of applicability for the application of supervised ML models in chemistry. In recent years, much work has been devoted to tackle the a) Electronic mail: anatole.vonlilienfeld@unibas.ch latter drawback, through the discovery and development of improved representations M. [9][10][11][12][13][14][15][16] For large N, errors of ML models have been found to decay inverse powers of N, 2 implying a linear relationship, log(Error) = a − b log(N). Therefore, the best representation must (i) minimize the off-set a and (ii) preserve the linearity in the second term while maximizing its pre-factor b.…”

Learning scheme to predict atomic forces and accelerate materials simulations

“…A new scheme is presented that systematically learns in an interpolative manner to predict atomic forces in environments encountered during the dynamical evolution of materials from a set of high-level calculations performed on reference atomic configurations with modest system sizes. This concept is resonant with emerging data-driven (or "big data" [2][3][4][5][6] ) approaches aimed at materials discovery in general 7,8 , as well as at accelerating materials simulations [9][10][11][12][13] . Machine learning (ML) methods using neural networks 9,10 and Gaussian processes 11,12 have been successful in the development of interatomic potentials, wherein the potential energy surface is learned from a set of higher-level (quantum mechanics based) reference calculations.…”

“…The distinctive aspect of the present contribution, namely, learning to predict atomic forces directly from past data has been suggested only recently 12,13 (to accelerate ab initio MD simulations on-the-fly). Here, we propose the creation of a stand-alone purely data-driven force prediction recipe (devoid of any explicit functional form), that can also provide the underlying potential energy surface (through integration).…”

“…Such a fingerprint should differentiate dissimilar configurations with adequate accuracy, and be invariant to transformations of the environment such as translation, rotation and permutation of like elements. While several such prescriptions have been proposed in the past [12][13][14][15][16][17][18] , the present objective, namely, mapping the vectorial force experienced by an atom to its configurational environment, places stringent constraints on the nature of the fingerprint. We argue that the following fingerprint function, V k i (η), may be used to accurately represent the k th component of the force on atom i 12 :…”

“…α t s and σ are the weight coefficients and length scale parameter, respectively. The optimal values for α t s and σ are determined during the training phase, with the help of crossvalidation and regularization methods 12,17,19,20 . Further details concerning the fingerprint construction and the learning algorithm can be found elsewhere 12 .…”