Interpolation and differentiation of alchemical degrees of freedom in machine learning interatomic potentials (2404.10746v3)

Abstract: Machine learning interatomic potentials (MLIPs) have become a workhorse of modern atomistic simulations, and recently published universal MLIPs, pre-trained on large datasets, have demonstrated remarkable accuracy and generalizability. However, the computational cost of MLIPs limits their applicability to chemically disordered systems requiring large simulation cells or to sample-intensive statistical methods. Here, we report the use of continuous and differentiable alchemical degrees of freedom in atomistic materials simulations, exploiting the fact that graph neural network MLIPs represent discrete elements as real-valued tensors. The proposed method introduces alchemical atoms with corresponding weights into the input graph, alongside modifications to the message-passing and readout mechanisms of MLIPs, and allows smooth interpolation between the compositional states of materials. The end-to-end differentiability of MLIPs enables efficient calculation of the gradient of energy with respect to the compositional weights. With this modification, we propose methodologies for optimizing the composition of solid solutions towards target macroscopic properties, characterizing order and disorder in multicomponent oxides, and conducting alchemical free energy simulations to quantify the free energy of vacancy formation and composition changes. The approach offers an avenue for extending the capabilities of universal MLIPs in the modeling of compositional disorder and characterizing the phase stability of complex materials systems.

Interpolation and Differentiation of Alchemical Degrees of Freedom in Machine Learning Interatomic Potentials

The paper explores the innovative incorporation of alchemical degrees of freedom within machine learning interatomic potentials (MLIPs) to enhance atomistic simulations of chemically complex systems. The authors address the challenges posed by conventional MLIPs, which, despite their accuracy and generalizability, struggle with computational costs in modeling large disordered systems or conducting extensive statistical sampling.

Core Contributions and Methodology

The central contribution is the methodical implementation of alchemical atoms within MLIPs, exploiting the graph-based nature of these models. The authors modify both the message-passing and readout stages of MLIPs to integrate continuous alchemical weights. This enables the interpolation between distinct compositional states by representing discrete elements as real-valued tensors within graph neural network architectures.

The proposed method provides a mechanism for calculating the gradient of energy concerning the compositional weights, thanks to the end-to-end differentiability of MLIPs. This capability is leveraged for optimizing the composition of solid solutions to target specific macroscopic properties and for conducting alchemical free energy simulations. The latter applications focus on quantifying the free energy changes associated with vacancy formation and compositional variations.

Numerical Results and Claims

Numerical studies demonstrate the method's applicability in cases involving solid solutions and free energy simulations. The approach successfully captures deviations from linear behavior in lattice parameter predictions, aligning with Vegard's law for some systems while identifying non-linearity for others. In the context of compositional optimization, the method allows for a straightforward gradient-based search over compositional space, showcasing computational efficiency relative to traditional enumeration methods.

Furthermore, the introduced alchemical path technique in free energy calculations yields consistent results with reduced variance compared to standard approaches like the Frenkel--Ladd path. The focus on statistical efficiency and reduced dissipated energies during simulations reinforces the practical advantages of this novel approach.

Practical and Theoretical Implications

Practically, integrating alchemical flexibility into MLIPs extends their usability for modeling material systems with compositional disorder, opening new avenues for materials design and optimization. This work represents an advancement in bridging machine learning with physical simulation, potentially leading to improved predictions in complex material systems where traditional theoretical models fall short.

Theoretically, the introduction of alchemical degrees of freedom enriches the MLIP framework, offering a nuanced approach to modeling the continuous change of elemental identities, a feature previously unexplored in such depth. The ability to interpolate smoothly between compositional states offers a new dimension for material property exploration, facilitating studies in phase stability and free energy landscapes.

Future Directions

The paper suggests future work integrating MLIPs with differentiable simulations and generative modeling frameworks to further exploit alchemical gradients for material discovery and optimization. As the landscape of machine learning in material science continues to evolve, such hybrid methods could yield deeper insights into the properties of materials and reinforce the MLIPs' role in computational materials science.

The research presents a comprehensive and technically robust approach to expanding the capabilities of MLIPs, setting the stage for advances in the simulation of compositional disorder and the design of novel materials. The implications of including alchemical flexibility in MLIPs are profound, with promising developments anticipated in both predictive accuracy and computational efficiency.