jaxhps
jaxhps: an elliptic PDE solver built with machine learning in mind
Science Score: 54.0%
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Repository
jaxhps: an elliptic PDE solver built with machine learning in mind
Basic Info
Statistics
- Stars: 5
- Watchers: 1
- Forks: 1
- Open Issues: 2
- Releases: 0
Metadata Files
README.md
jaxhps
A JAX package implementing hardware acceleration for HPS methods in two and three dimensions.
See our preprint on arXiv: Hardware Acceleration for HPS Methods in Two and Three Dimensions
Installation
To install, you can use pip:
pip install jaxhps
The examples require additional packages matplotlib and h5py. If you want to install them automatically, use:
pip install jaxhps[examples]
Documentation
https://jaxhps.readthedocs.io/en/latest/
Examples
hp convergence on 2D problems with known solutions
Shows convergence using uniform quadtrees using both DtN matrices and ItI matrices.
python examples/hp_convergence_2D_problems.py --DtN --ItI
High-wavenumber scattering problem
First, run the matlab script examples/driver_gen_SD_matrices.m. This will generate and save exterior single and double-layer kernel matrices. These matrices are necessary to define a boundary integral equation for the scattering problem.
Once in place, we can run the script:
python examples/wave_scattering_compute_reference_soln.py --scattering_potential gauss_bumps -k 100 --plot_utot
This will generate plots which looks like this, showing the scattering potential and real part and modulus of the total field:
Adaptive discretization on a 3D problem with known solution
We have a script for generating adaptive discretizations on the wavefront problem presented in our paper:
python examples/wavefront_adaptive_discretization_3D.py -p 10 --tol 1e-02 1e-05
This should produce an image showing the computed solution, generated grid, and error map:
Inverse wave scattering using automatic differentiation
We have an implementation of a low-dimensional optimization problem using automatic differentiation:
python examples/inverse_wave_scattering.py --n_iter 25
This is an inverse scattering problem where we try to recover the locations of four Gaussian bumps which make up the scattering potential. Running the code should produce plots showing the optimization variables converging at the centers of the Gaussian bumps in the scattering potential, as well as a plot showing the convergence of the objective function:
Linearized Poisson--Boltzmann equation
Our method can be used to solve the a linearized Poisson-Boltzmann equation, which models the electrostatic properties of a molecule in solution.
python examples/poisson_boltzmann_example.py --tol 1e-01 1e-03 -p 10
Owner
- Login: meliao
- Kind: user
- Location: Chicago, IL
- Repositories: 2
- Profile: https://github.com/meliao
Hi! I'm a graduate student at UChicago CS studying machine learning theory.
JOSS Publication
jaxhps: An elliptic PDE solver built with machine learning in mind
Authors
Center for Computational Mathematics, Flatiron Institute, USA
Center for Computational Mathematics, Flatiron Institute, USA, Center for Computational Biology, Flatiron Institute, USA
Computational and Applied Mathematics, Department of Statistics, University of Chicago, USA
Computational and Applied Mathematics, Department of Statistics, University of Chicago, USA, Department of Computer Science, University of Chicago, USA, Data Science Institute, University of Chicago, USA
Editor
Anjali Sandip
Tags
JAX numerical analysis partial differential equations scientific computingCitation (CITATION.cff)
cff-version: 1.2.0
message: If you use this software, please cite both the article from preferred-citation and the software itself.
authors:
- family-names: Melia
given-names: Owen
- family-names: Fortunato
given-names: Daniel
- family-names: Jeremy
given-names: Hoskins
- family-names: Rebecca
given-names: Willett
title: Hardware Acceleration for HPS Algorithms in Two and Three Dimensions
version: 1.0.0
url: https://github.com/meliao/jaxhps
date-released: '2025-03-28'
preferred-citation:
authors:
- family-names: Melia
given-names: Owen
- family-names: Fortunato
given-names: Daniel
- family-names: Jeremy
given-names: Hoskins
- family-names: Rebecca
given-names: Willett
title: Hardware Acceleration for HPS Algorithms in Two and Three Dimensions
url: https://arxiv.org/abs/2503.17535
type: generic
year: '2025'
conference: {}
publisher: {}
GitHub Events
Total
- Issues event: 1
- Watch event: 3
- Delete event: 2
- Push event: 11
- Pull request event: 3
- Fork event: 1
- Create event: 5
Last Year
- Issues event: 1
- Watch event: 3
- Delete event: 2
- Push event: 11
- Pull request event: 3
- Fork event: 1
- Create event: 5
Packages
- Total packages: 1
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Total downloads:
- pypi 32 last-month
- Total dependent packages: 0
- Total dependent repositories: 0
- Total versions: 2
- Total maintainers: 1
pypi.org: jaxhps
An elliptic PDE solver built with machine learning in mind
- Documentation: https://jaxhps.readthedocs.io/
- License: mit
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Latest release: 0.1
published 8 months ago
Rankings
Maintainers (1)
Dependencies
- actions/checkout v3 composite
- actions/setup-python v3 composite