High-dimensional potential energy surfaces for molecular simulations: from empiricism to machine learning

Abstract

An overview of computational methods to describe high-dimensional potential energy surfaces suitable for atomistic simulations is given. Particular emphasis is put on accuracy, computability, transferability and extensibility of the methods discussed. They include empirical force fields, representations based on reproducing kernels, using permutationally invariant polynomials, neural network-learned representations and combinations thereof. Future directions and potential improvements are discussed primarily from a practical, application-oriented perspective.

A transferable active-learning strategy for reactive molecular force fields

“…However, because of their high computational cost and unfavourable scaling behaviour, they are limited to a few hundred atoms and simulation times of picoseconds in ab initio molecular dynamics (AIMD) at the DFT level, and practically impossible at the computational 'gold-standard' [CCSD(T)]. 3 Machine learning (ML) approaches have the potential to revolutionise force-field based simulations, aiming to provide the best of both worlds, [4][5][6] and have indeed begun to provide new insights into a range of challenging research problems. [7][8][9][10][11][12][13][14][15][16] The development of an ML potential applicable to the whole periodic table mapping nuclear coordinates to total energies and forces is, however, precluded by the curse of dimensionality.…”

“…[7][8][9][10][11][12][13][14][15][16] The development of an ML potential applicable to the whole periodic table mapping nuclear coordinates to total energies and forces is, however, precluded by the curse of dimensionality. Within small chemical subspaces, models can be achieved using neural networks (NNs), 6,[17][18][19][20][21] kernel-based methods such as the Gaussian Approximation Potential (GAP) framework 22,23 or gradient-domain machine learning (GDML), 24 and linear fitting with properly chosen basis functions, 25,26 each with different data requirements and transferability. 27 GAPs have been used to study a range of elemental, [28][29][30] multicomponent inorganic, 31,32 gas-phase organic molecular, 13,33 and more recently condensed-phase systems, such as methane 34 and phosphorus.…”

A Transferable Active-Learning Strategy for Reactive Molecular Force Fields

“…In contrast, ab initio methods provide an accurate description of the potential-energy surface (PES) -which is particularly critical for reactions in solutionbut, because of their high computational cost and unfavourable scaling behaviour, are limited to a few hundred atoms and simulation times of picoseconds in ab initio molecular dynamics (AIMD). 3 Machine learning (ML) approaches have the potential to revolutionize force-field based simulations, aiming to provide the best of both worlds, [4][5][6] and have indeed begun to provide new insights into a range of challenging research problems. [7][8][9][10][11][12][13][14][15] The development of a truly general ML potential mapping nuclear coordinates to total energies and forces is, however, precluded by the curse of dimensionality.…”

“…[7][8][9][10][11][12][13][14][15] The development of a truly general ML potential mapping nuclear coordinates to total energies and forces is, however, precluded by the curse of dimensionality. Within small chemical subspaces, models can be achieved using neural networks (NNs), 6,[16][17][18][19][20] kernel-based methods such as Gaussian processes (GP) 21,22 and gradient-domain machine learning (GDML), 23 and linear fitting with properly chosen basis functions, 24,25 each with different data requirements and transferability. 26 In the present work, we employ the Gaussian Approximation Potential (GAP) framework, 21 which has been used to generate force fields for a range of elemental, [27][28][29] multicomponent inorganic, 30,31 and recently gas-phase organic systems.…”

Automated Construction of Neural Network Potential Energy Surface: The Enhanced Self-Organizing Incremental Neural Network Deep Potential Method

“…Among them, the artificial NN is the most promising one, which in principle is able to approximate any real-valued function to arbitrary accuracy 16 . And it has been used in many important physical or chemical questions [17][18][19][20][21][22][23][24][25][26][27][28][29] .…”