Surrogate Hessian Relax is a Python implementation of The Surrogate Hessian Accelerated Parallel Line-search. The method is inteded for optimizing and performing energy minimization of atomic structures in the presence of statistical noise.
NOTE: the implementation is currently in an early stage of development.
The method has been published in The Journal of Chemical Physics as Surrogate Hessian Accelerated Structural Optimization for Stochastic Electronic Structure Theories
Upon publishing results based on the method, we kindly ask you to cite
Juha Tiihonen, Paul R. C. Kent, and Jaron T. Krogel
The Journal of Chemical Physics
156, 054104 (2022)
The Surrogate Hessian Accelerated Parallel Line-search is an algorithm for relaxing atomic structures by energy minimization, in the presence of statistical noise. It is based on conjugate gradient descent (or parallel line-search), and using a surrogate method to characterize the potential energy surface (PES).
For more details on the scope and the theoretical background, we refer to the Original work.
The energy minimization involves two electronic structure theories or methods, which will be called the Surrogate and the Stochastic method. The Surrogate method is cheap and smooth but has limited accuracy, such as Density Functional Theory (DFT). The Stochastic method has higher accuracy but is more costly to evaluate and subject to statistical noise, such as Quantum Monte Carlo (QMC).
An overview of the algorithm is presented below in a simplified graph:
The structural relaxation is indeed done in five steps:
- Surrogate: Relaxation
- Surrogate: Parameter Hessian
- Surrogate: Line-search optimization
- Stochastic: Line-search
- Stochastic: Finding new minimum
Background and instructions for setting up each of the steps is given in the main Documentation (work-in-progress).
To install, make sure to meet the following minimum requirements for Python.
- Python (3.12.5)
- Numpy (2.0.1)
- Scipy (1.14.1)
- Dill (0.3.9)
- Matplotlib (3.9.2)
- Nexus (https://qmcpack.org)
The libraries of Nexus and the root directory of Surrogate Hessian Relax,
containing surrogate_tools.py, surrogate_relax.py, and
surrogate_error_scan.py need to be in the Python environment.
For instance, include these locations in the PYTHONPATH variable.
The support of various Surrogate and Stochastic methods is currently implemented through Nexus. The following list contains the software and methods with which the toolbox has been used and which are covered in the present set of examples:
-
Surrogate methods:
- Quantum Espresso (https://https://www.quantum-espresso.org/)
-
Stochastic methods:
- QMCPACK (https://qmcpack.org)
However, it is possible to use Surrogate Hessian Relax without direct Nexus support (will be documented).
List of scientific works demonstrating the The Surrogate Hessian Accelerated Parallel Line-search method:
- J. Chem. Phys, 156, 054104 (2022) Surrogate Hessian Accelerated Structural Optimization for Stochastic Electronic Structure Theories
- J. Chem. Phys. 156, 014707 (2022) A combined first principles study of the structural, magnetic, and phonon properties of monolayer CrI3
- Phys. Rev. Materials 5, 024002 (2021) Optimized structure and electronic band gap of monolayer GeSe from quantum Monte Carlo methods
While the theoretical method has been successfully demonstrated, the software implementation is currently under major development.
On one hand this means that unexperiences users should expect some troubleshooting before successful completion of a line-search project. On the other hand, the code design and conventions will be subject to change until the first stable version is published.
Support can be inquired by contacting the authors.
The authors of this method are Juha Tiihonen, Paul R. C. Kent and Jaron T. Krogel, working in the Center for Predictive Simulation of Functional Materials (https://cpsfm.ornl.gov/)
This work has been authored in part by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE).