The length and time scales of atomistic simulations are limited by the computational cost of the methods used to predict material properties. In recent years there has been great progress in the use of machine-learning algorithms to develop fast and accurate interatomic potential models, but it remains a challenge to develop models that generalize well and are fast enough to be used at extreme time and length scales. To address this challenge, we have developed a machine-learning algorithm based on symbolic regression in the form of genetic programming that is capable of discovering accurate, computationally efficient many-body potential models. The key to our approach is to explore a hypothesis space of models based on fundamental physical principles and select models within this hypothesis space based on their accuracy, speed, and simplicity. The focus on simplicity reduces the risk of overfitting the training data and increases the chances of discovering a model that generalizes well. Our algorithm was validated by rediscovering an exact Lennard-Jones potential and a Sutton-Chen embedded-atom method potential from training data generated using these models. By using training data generated from density functional theory calculations, we found potential models for elemental copper that are simple, as fast as embedded-atom models, and capable of accurately predicting properties outside of their training set. Our approach requires relatively small sets of training data, making it possible to generate training data using highly accurate methods at a reasonable computational cost. We present our approach, the forms of the discovered models, and assessments of their transferability, accuracy and speed.

原子模拟的时间尺度和时间尺度受到用于预测材料性能的方法的计算成本的限制。近年来，在使用机器学习算法来开发快速而准确的原子间电势模型方面取得了巨大的进步，但是，要开发一种能够很好地推广并且能够在极端的时间和长度尺度下使用的足够快的模型，仍然是一个挑战。为了解决这一挑战，我们开发了一种基于符号回归的机器学习算法，该算法以遗传编程的形式进行，能够发现准确，计算效率高的多体潜能模型。我们方法的关键是基于基本物理原理探索模型的假设空间，并根据其准确性，速度和简单性在该假设空间中选择模型。对简单性的关注减少了过度拟合训练数据的风险，并增加了发现泛化效果好的模型的机会。通过从使用这些模型生成的训练数据中重新发现确切的Lennard-Jones势和Sutton-Chen嵌入原子方法势来验证了我们的算法。通过使用从密度泛函理论计算中生成的训练数据，我们发现了元素铜的潜在模型，该模型简单，与嵌入原子模型一样快，并且能够准确地预测其训练集之外的属性。我们的方法需要相对较少的训练数据集，从而有可能以合理的计算成本使用高度精确的方法来生成训练数据。我们介绍了我们的方法，发现的模型的形式以及对它们可移植性的评估，