immrax

immrax is a tool for interval analysis and mixed monotone reachability analysis in JAX.

Inclusion function transformations are composable with existing JAX transformations, allowing the use of Automatic Differentiation to learn relationships between inputs and outputs, as well as parallelization and GPU capabilities for quick, accurate reachable set estimation.

For more information, please see the full documentation.

Dependencies

immrax depends on the library pypoman, which internally uses pycddlib as a wrapper around the cdd library. For this wrapper to function properly, you must install cdd to your system. On Ubuntu, the relevant packages can be installed with

apt-get install -y libcdd-dev libgmp-dev

On Arch linux, you can use

pacman -S cddlib

Installation

Setting up a conda environment

We recommend installing JAX and immrax into a conda environment (miniconda).

conda create -n immrax python=3.12
conda activate immrax

Installing immrax

immrax is available as a package on PyPI and can be installed with pip.

pip install immrax

If you have cuda-enabled hardware you wish to utilize, please install the cuda optional dependency group.

...
pip install immrax[cuda]

To test if the installation process worked, run the compare.py example. The additional examples optional dependency group contains some dependencies needed for the more complex examples; be sure to also install it if you want to run the others.

cd examples
python compare.py

This should return the outputs of different inclusion functions as well as their runtimes.

Citation

If you find this library useful, please cite our paper with the following bibtex entry.

@article{immrax,
title = {immrax: A Parallelizable and Differentiable Toolbox for Interval Analysis and Mixed Monotone Reachability in {JAX}},
journal = {IFAC-PapersOnLine},
volume = {58},
number = {11},
pages = {75-80},
year = {2024},
note = {8th IFAC Conference on Analysis and Design of Hybrid Systems ADHS 2024},
issn = {2405-8963},
doi = {https://doi.org/10.1016/j.ifacol.2024.07.428},
url = {https://www.sciencedirect.com/science/article/pii/S2405896324005275},
author = {Akash Harapanahalli and Saber Jafarpour and Samuel Coogan},
keywords = {Interval analysis, Reachability analysis, Automatic differentiation, Parallel computation, Computational tools, Optimal control, Robust control},
abstract = {We present an implementation of interval analysis and mixed monotone interval reachability analysis as function transforms in Python, fully composable with the computational framework JAX. The resulting toolbox inherits several key features from JAX, including computational efficiency through Just-In-Time Compilation, GPU acceleration for quick parallelized computations, and Automatic Differentiability We demonstrate the toolbox’s performance on several case studies, including a reachability problem on a vehicle model controlled by a neural network, and a robust closed-loop optimal control problem for a swinging pendulum.}
}