Surrogate Theory Accelerated Line-search Kit (STALK)

Surrogate Theory Accelerated Line-search Kit (STALK) is a Python implementation of The Surrogate Hessian Accelerated Parallel Line-search method. The method is intended for local optimization of noisy, multivariable cost functions that can be approximated with a surrogate model. It has the following features:

• Robust: rarely misses the minimum
• Fast to converge: requires minimal iterations to solution
• Controllable accuracy: can be tuned to the desired accuracy
• Cost-efficient: meets the accuracy with minimal statistical sampling
• Parallelizable: numerous evaluations may run in parallel

Typical applications of STALK include:

• Relaxation of atomic structures with noisy energies, e.g., quantum Monte Carlo.
• Optimization of variational quantum eigensolvers

Advanced features include:

• Statistical analyses of black-box cost functions and line-searches
• Treatment of low-dimensional parametric spaces, Hessians, etc
• Gradient-free transition pathway search

GETTING STARTED

The code can be installed with pip from PyPi

pip install stalk-qmc

See the installation instructions for more details.

Installation comprises various methods in the stalk package, for example:

# Using line-search along 45 degree direction, find the minimum of a simple 2D function
import numpy as np
from stalk import ParameterSet, PesFunction, LineSearch

def my_pes(x: ParameterSet) -> float:
    return (x.params[0])**2 + (x.params[1])**2

pes = PesFunction(my_pes)
p = ParameterSet([2.0, 2.0])
direction = np.array([0.5, 0.5])**0.5
sigma = 0.1  # statistical noise
ls = LineSearch(p, direction=direction, R=4.0, M=7, sigma=sigma)
pes(ls, add_sigma=True)
print(ls)
# The true solution (0, 0) is solved relative to the line-search starting point (2, 2)
# ls.x0 ~ -1 ± 0.05
# ls.y0 ~ -2**1.5 ± 0.1
p0 = p.copy()
p0.shift_params(ls.x0 * direction)
print(p0.params)
# p0.params ~ [0.0, 0.0]

See Documentation (WIP) to learn the basic concepts, algorithms and operating principles of the code.

See examples to study comprehensive workflows of the code, including geometry relaxation, transition pathway search and optimization of the variational quantum eigensolver.

CITING

Upon publishing results based on the method, we kindly ask you to cite The original work.

Juha Tiihonen, Paul R. C. Kent, and Jaron T. Krogel
The Journal of Chemical Physics
156, 054104 (2022)

SUPPORT

The software and its documentation are under development with no warranties. Support may be inquired by contacting the authors.

ACKNOWLEDGEMENTS

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/)

The code is written and developed by:

• Juha Tiihonen

Contributions to the algorithms have been made by:

• Jaron T. Krogel
• Gopal Iyer
• Simon Nirenberg

Further contributions are always welcome.

This work has been authored in part by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE).