Inverse Design of Materials Using Automatic Differentiation: From Model Hamiltonians to First-Principles Calculations
ORAL · Invited
Abstract
The ultimate goal of materials science is to design and create materials with desired physical properties. In recent years, inverse-design approaches that start from target properties and construct materials or models have attracted growing interest. Previous work includes machine-learning-based methods such as Bayesian optimization, generative models, and genetic algorithms, and perturbative analytical schemes, but these typically require large datasets and computational resources, struggle with extrapolation, and are limited in the properties they can treat.
We have developed an inverse-design framework for materials systems that uses automatic differentiation in physical numerical calculations. This framework can be applied to a wide variety of physical properties, avoids the need for large datasets, and removes extrapolation issues by optimizing physical calculations that obey the underlying equations.
We first introduce a scheme that automatically constructs model Hamiltonians realizing prescribed properties. Designing a system with a large anomalous Hall effect leads to the “rediscovery” of the Haldane model and to the construction of new models with large Chern numbers. The same framework applies to diverse targets, including photovoltaic response, quantum entanglement, and magnetoresistance.
We then extend this inverse design to first-principles DFT calculations with the KKR+CPA method. KKR+CPA naturally represents compositions as continuous variables, which is well suited to automatic-differentiation-based optimization. We automatically narrow down, from many candidate compositions, materials that satisfy desired properties. In a search over 30-component systems, the method identifies magnetic materials, and for a given host it simultaneously determines impurity species and doping levels.
We conclude with prospects for applying this framework to broader classes of materials and phenomena.
We have developed an inverse-design framework for materials systems that uses automatic differentiation in physical numerical calculations. This framework can be applied to a wide variety of physical properties, avoids the need for large datasets, and removes extrapolation issues by optimizing physical calculations that obey the underlying equations.
We first introduce a scheme that automatically constructs model Hamiltonians realizing prescribed properties. Designing a system with a large anomalous Hall effect leads to the “rediscovery” of the Haldane model and to the construction of new models with large Chern numbers. The same framework applies to diverse targets, including photovoltaic response, quantum entanglement, and magnetoresistance.
We then extend this inverse design to first-principles DFT calculations with the KKR+CPA method. KKR+CPA naturally represents compositions as continuous variables, which is well suited to automatic-differentiation-based optimization. We automatically narrow down, from many candidate compositions, materials that satisfy desired properties. In a search over 30-component systems, the method identifies magnetic materials, and for a given host it simultaneously determines impurity species and doping levels.
We conclude with prospects for applying this framework to broader classes of materials and phenomena.
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Publication: Koji Inui and Yukitoshi Motome, "Inverse Hamiltonian design by automatic differentiation", Commun. Phys. 6, 37 (2023)
Koji Inui and Yukitoshi Motome, "Inverse Hamiltonian design of highly entangled quantum systems", Phys. Rev. Research 6, 033080 (2024)
Yuta Hirasaki, Koji Inui, and Eiji Saitoh, "Inverse magnetoconductance design by automatic differentiation", Phys. Rev. B 110, 214201 (2024)
Kohei Ishii, Hisazumi Akai, Tetsuya Fukushima, Hikari Shinya, and Koji Inui, in preparation
Presenters
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Koji Inui
- The University of Tokyo