Algorithmic differentiation for plane-wave DFT: materials design, error control and learning model parameters
arXiv:2509.07785 · doi:10.1038/s41524-025-01880-3
Abstract
We present a differentiation framework for plane-wave density-functional theory (DFT) that combines the strengths of forward-mode algorithmic differentiation (AD) and density-functional perturbation theory (DFPT). In the resulting AD-DFPT framework derivatives of any DFT output quantity with respect to any input parameter (e.g. geometry, density functional or pseudopotential) can be computed accurately without deriving gradient expressions by hand. We implement AD-DFPT into the Density-Functional ToolKit (DFTK) and show its broad applicability. Amongst others we consider the inverse design of a semiconductor band gap, the learning of exchange-correlation functional parameters, or the propagation of DFT parameter uncertainties to relaxed structures. These examples demonstrate a number of promising research avenues opened by gradient-driven workflows in first-principles materials modeling.
22 pages, 9 figures. Code available at https://github.com/niklasschmitz/ad-dfpt (archived copy at https://zenodo.org/records/17084313)
References in corpus (43)
- Restoring the density-gradient expansion for exchange in solids and surfaces
- Generalized gradient approximation for solids and their surfaces
- CP2K: An Electronic Structure and Molecular Dynamics Software Package -- Quickstep: Efficient and Accurate Electronic Structure Calculations
- Optimized norm-conserving Vanderbilt pseudopotentials
- The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table
- Quantum ESPRESSO toward the exascale
- Pseudopotentials for high-throughput DFT calculations
- Optimization Algorithm for the Generation of ONCV Pseudopotentials
- Implementation strategies in phonopy and phono3py
- Systematic treatment of displacements, strains and electric fields in density-functional perturbation theory
- Precision and efficiency in solid-state pseudopotential calculations
- Finding Density Functionals with Machine Learning
- Metric Tensor Formulation of Strain in Density-Functional Perturbation Theory
- Deep-Learning Density Functional Theory Hamiltonian for Efficient ab initio Electronic-Structure Calculation
- Bayesian Error Estimation in Density Functional Theory
- Kohn-Sham equations as regularizer: building prior knowledge into machine-learned physics
- Hole mobility of strained GaN from first principles
- A Differentiable Programming System to Bridge Machine Learning and Scientific Computing
- Learning the exchange-correlation functional from nature with fully differentiable density functional theory
- DeePKS: a comprehensive data-driven approach towards chemically accurate density functional theory
- How to verify the precision of density-functional-theory implementations via reproducible and universal workflows
- Differentiable sampling of molecular geometries with uncertainty-based adversarial attacks
- Precise effective masses from density functional perturbation theory
- DQC: a Python program package for Differentiable Quantum Chemistry
- Differentiable quantum chemistry with PySCF for molecules and materials at the mean-field level and beyond
- Differentiable Molecular Simulations for Control and Learning
- Automated all-functionals infrared and Raman spectra
- Neural-network Density Functional Theory Based on Variational Energy Minimization
- Grad DFT: a software library for machine learning enhanced density functional theory
- Automatic Differentiation for Orbital-Free Density Functional Theory
- Stress and heat flux via automatic differentiation
- Inverse molecular design and parameter optimization with Hückel theory using automatic differentiation
- Algorithmic Differentiation for Automated Modeling of Machine Learned Force Fields
- Variational Density Functional Perturbation Theory for Metals
- Addressing the Band Gap Problem with a Machine-Learned Exchange Functional
- PET-MAD, a lightweight universal interatomic potential for advanced materials modeling
- Uncertainty of DFT calculated mechanical and structural properties of solids due to incompatibility of pseudopotentials and exchange-correlation functionals
- Accurate and scalable exchange-correlation with deep learning
- Differentiable Programming for Differential Equations: A Review
- The Elements of Differentiable Programming
- Numerical stability and efficiency of response property calculations in density functional theory
- Practical error bounds for properties in plane-wave electronic structure calculations
- Density-Functional Perturbation Theory with Numeric Atom-Centered Orbitals