Exploring the necessary complexity of interatomic potentials

Highlights

• Spline-based potentials provide a framework for a systematically-improvable model.

• These potentials can achieve near-DFT accuracies with classical potential speeds.

• The Pareto front is dominated by spline MEAM and moment tensor potentials.

• Custom data structures make fitting spline-based potentials fast and scalable.

Abstract

The application of machine learning models and algorithms towards describing atomic interactions has been a major area of interest in materials simulations in recent years, as machine learning interatomic potentials (MLIPs) are seen as being more flexible and accurate than their classical potential counterparts. This increase in accuracy of MLIPs over classical potentials has come at the cost of significantly increased complexity, leading to higher computational costs and lower physical interpretability and spurring research into improving the speeds and interpretability of MLIPs. As an alternative, in this work we leverage “machine learning” fitting databases and advanced optimization algorithms to fit a class of spline-based classical potentials, showing that they can be systematically improved in order to achieve accuracies comparable to those of low-complexity MLIPs. These results demonstrate that high model complexities may not be strictly necessary in order to achieve near-DFT accuracy in interatomic potentials and suggest an alternative route towards sampling the high accuracy, low complexity region of model space by starting with forms that promote simpler and more interpretable interatomic potentials.

Introduction

For nearly a century of designing interatomic potentials for use in materials simulations, a strong emphasis was placed on constructing classical potentials with physically-motivated forms derived from quantum mechanical theories [1], [2], [3], [4], [5], [6], [7], [8], [9]. More recently, with the enormous success of machine learning in various fields, machine learning interatomic potentials (MLIPs) have come to dominate the attention of the computational materials science community (an incomplete list: [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20]). MLIPs have been shown to be able to predict energies and forces on diverse ranges of atomic configurations with unprecedented accuracy, which in combination with active research into improving their speed and interpretability [21], [22], [23] makes them good candidates for being fast and accurate general-purpose models of atomic interactions.

Much of the increased performance of MLIPs over classical potentials comes from the flexibility in their functional forms that allows them to be systematically extended in order to be able to model increasingly diverse sets of atomic environments. However, pushing MLIPs to this limit of high accuracy and generalizability often results in highly complex models that are computationally expensive to use and conceptually difficult to interpret. Classical potentials, on the other hand, are by construction much simpler to interpret due to their basis in known physics and usually have much lower computational costs than even the simplest MLIPs. These two forms thus are generally used in opposing regions of “model space”: classical potentials in the low complexity, low accuracy region; MLIPs in the high complexity, high accuracy region.

Sampling the space between these two regions (low complexity, high accuracy) is a fundamental goal of computational materials science, and in recent years has most often been approached by attempting to decrease the complexity of MLIPs. In this work we show that a family of spline-based classical potentials, when leveraging traditional “machine learning” databases and fitting algorithms, can be systematically improved in order to achieve accuracies on existing benchmark databases that push them into the low complexity, high accuracy region of model space alongside low-complexity MLIPs. Despite the lower interpretability of spline-based potentials relative to classical potentials with explicit analytical definitions, our results show that spline-based classical potentials offer a good balance between speed, interpretability, and accuracy. These results suggest that spline-based classical potentials may be good options alongside low-complexity MLIPs for designing practical and computationally tractable general-purpose potentials.