Active and Transfer Learning of High-Dimensional Neural Network Potentials for Transition Metals.

Classical molecular dynamics (MD) simulations represent a very popular and powerful tool for materials modeling and design. The predictive power of MD hinges on the ability of the interatomic potential to capture the underlying physics and chemistry. There have been decades of seminal work on developing interatomic potentials, albeit with a focus predominantly on capturing the properties of bulk materials. Such physics-based models, while extensively deployed for predicting the dynamics and properties of nanoscale systems over the past two decades, tend to perform poorly in predicting nanoscale potential energy surfaces (PESs) when compared to high-fidelity first-principles calculations. These limitations stem from the lack of flexibility in such models, which rely on a predefined functional form. Machine learning (ML) models and approaches have emerged as a viable alternative to capture the diverse size-dependent cluster geometries, nanoscale dynamics, and the complex nanoscale PESs, without sacrificing the bulk properties. Here, we introduce an ML workflow that combines transfer and active learning strategies to develop high-dimensional neural networks (NNs) for capturing the cluster and bulk properties for several different transition metals with applications in catalysis, microelectronics, and energy storage, to name a few. Our NN first learns the bulk PES from the high-quality physics-based models in literature and subsequently augments this learning via retraining with a higher-fidelity first-principles training data set to concurrently capture both the nanoscale and bulk PES. Our workflow departs from status-quo in its ability to learn from a sparsely sampled data set that nonetheless covers a diverse range of cluster configurations from near-equilibrium to highly nonequilibrium as well as learning strategies that iteratively improve the fingerprinting depending on model fidelity. All the developed models are rigorously tested against an extensive first-principles data set of energies and forces of cluster configurations as well as several properties of bulk configurations for 10 different transition metals. Our approach is material agnostic and provides a methodology to transfer and build upon the learnings from decades of seminal work in molecular simulations on to a new generation of ML-trained potentials to accelerate materials discovery and design.

Learning in continuous action space for developing high dimensional potential energy models.

Reinforcement learning (RL) approaches that combine a tree search with deep learning have found remarkable success in searching exorbitantly large, albeit discrete action spaces, as in chess, Shogi and Go. Many real-world materials discovery and design applications, however, involve multi-dimensional search problems and learning domains that have continuous action spaces. Exploring high-dimensional potential energy models of materials is an example. Traditionally, these searches are time consuming (often several years for a single bulk system) and driven by human intuition and/or expertise and more recently by global/local optimization searches that have issues with convergence and/or do not scale well with the search dimensionality. Here, in a departure from discrete action and other gradient-based approaches, we introduce a RL strategy based on decision trees that incorporates modified rewards for improved exploration, efficient sampling during playouts and a "window scaling scheme" for enhanced exploitation, to enable efficient and scalable search for continuous action space problems. Using high-dimensional artificial landscapes and control RL problems, we successfully benchmark our approach against popular global optimization schemes and state of the art policy gradient methods, respectively. We demonstrate its efficacy to parameterize potential models (physics based and high-dimensional neural networks) for 54 different elemental systems across the periodic table as well as alloys. We analyze error trends across different elements in the latent space and trace their origin to elemental structural diversity and the smoothness of the element energy surface. Broadly, our RL strategy will be applicable to many other physical science problems involving search over continuous action spaces.