Higher-Order Bayesian Optimization (HOBO)

This repository provides code for Higher-Order Bayesian Optimization (HOBO) — a framework for optimizing functions for which derivative information (gradients and Hessians) is available, e.g., through adjoint or automatic differentiation.

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Overview

The code constructs a Gaussian Process (GP) surrogate model from available training data:

• 0th order: inputs and function value observations
• 1st order: inputs with function values and gradients
• 2nd order: inputs with function values, gradients, and Hessians

The surrogate model guides sampling in the design space via an acquisition function, which determines where to sample next. The objective is to efficiently identify extrema of the underlying function by leveraging higher-order information.

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Applications

HOBO enables global optimization of functions for which derivative observations (currently up to second order) can be obtained.
The structure is designed to be general-purpose and adaptable to different optimization problems.

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Repository Structure

• hobo/ – Core implementation
  • hobo_config/config_defaults.py: main configuration options
• tutorials/ – Example scripts and demos
  • tutorials/hobo_demo.py: recommended starting point
• hobo/hobo_test_functions/ – Analytical test functions for benchmarking

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Installation

HOBO builds upon:

• BoTorch – Bayesian optimization framework
• GPyTorch – Gaussian Process modeling
• PyTorch – automatic differentiation backend

To install HOBO as a Python package:

git clone https://github.com/mreumi/HOBO.git
cd HOBO
pip install -e .

After installation, you can import HOBO as:

import hobo

Usage

All settings are controlled through the configuration system in
hobo/hobo_config/config_defaults.py.

For a quick start, run the demo:

python tutorials/hobo_demo.py

Citation

If you use this code in your research, please cite:

Reumschüssel, J. M., et al. (2025).
Shape Optimization for Control of Coherent Structures using Linear Analysis and Higher-Order Bayesian Optimization.
Journal of Computational Physics.
DOI: to be determined

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Contact

Developed and maintained by Moritz Reumschüssel
For questions or discussions, please contact: reumschuessel@tu-berlin.de