acropora

acropora evolves probability measures by pushing forward individual states. It approximates statistical solutions of nonlinear PDEs by propagating Monte Carlo ensembles through deterministic solvers, on CPU (NumPy) or GPU (CuPy) from a single code path. Its first scheme is a vectorial lattice Boltzmann method for the compressible Euler equations used in the reference application to compute statistical solutions of a Mach 2000 astrophysical jet.

acropora is the companion code to: S. Simonis and G. Wissocq, Computing statistical solutions of a Mach 2000 astrophysical jet, arXiv:2605.25282 (2026). url: https://arxiv.org/abs/2605.25282 doi: 10.48550/arXiv.2605.25282

The data of the paper are archived on Zenodo: doi: 10.5281/zenodo.23415318

Install

Requires Python 3.9 or newer.

git clone https://github.com/stephan-911/acropora.git
cd acropora
pip install -e .              # CPU only
pip install -e ".[gpu]"       # + CuPy (CUDA 12)
pip install -e ".[post,dev]"  # post-processing / tests
python -m pytest tests -q     # 33 passed

On a cluster, load a recent Python first (module load ...; for the GPU extra also the CUDA 12 module) and place the virtual environment on a work filesystem:

python3 -m venv $WORK/acropora-venv
$WORK/acropora-venv/bin/pip install --upgrade pip
$WORK/acropora-venv/bin/pip install -e "/path/to/acropora[post,dev]"

An editable install records the repository path, so the environment keeps tracking the checkout wherever it sits. The batch jobs take the environment from VENV in the site file (see Batch jobs).

Quick start (CPU)

import numpy as np
from acropora import (Euler2D, VectorialD2Q5, Mach2000JetBC, run_sample,
                     grid_from_nx)

Nx, Ny, dx = grid_from_nx(250)          # 250 x 200 cells, dx = 0.01
bc = Mach2000JetBC.make("ghost", Ny, seed=42)          # portable RNG
solver = VectorialD2Q5(Euler2D(gamma=5/3), Nx, Ny, dx,
                       xp=np, boundary=bc)
bc.initial_condition(solver)
run_sample(solver, np.linspace(0, 0.0035, 8),
           lambda ck, rho: print(ck, rho.max()))

Switch to GPU by xp = acropora.get_xp("gpu") (or --backend gpu in the example CLI); nothing else changes.

Layout

src/acropora/
  backend.py          array-namespace dispatch (numpy/cupy), device mgmt
  grid.py             grid geometry from the x-resolution Nx
  random_fields.py    stochastic inlet perturbation + RNG modes
  models/             PDE systems: fluxes + wave-speed bound (Euler2D; add
                      your system here)
  schemes/            time-stepping schemes (vectorial D2Q5 with
                      positivity limiter; add schemes here)
  limiters.py         reusable limiter components
  boundaries.py       boundary/IC objects (Mach2000JetBC; add setups here)
  runner.py           single-sample time loop + checkpointing
  ensemble.py         Monte Carlo orchestration (node partitioning,
                      per-sample restart, persistent worker pool)
  io/                 memmapped ensemble store
  post/               post-processing: grid restriction, one-/
                      two-point Wasserstein distances, strong L1 error,
                      mean/std errors, rate fits, part merging,
                      centerline bands and one-point densities,
                      PDF-heatmap rasterization with pgfplots output,
                      quantile-band diagnostics
examples/mach2000_jet/  CLI + SLURM script for reproducibility
baseline/             reference implementation behind a numpy shim
                      (regression baseline)
tests/                bit-exact regression vs baseline + physics tests
benchmarks/           CPU benchmark + cluster GPU benchmark/repro script

The split: a model provides fluxes and a wave-speed bound, a scheme integrates any model, and a boundary object owns setup-specific state, so a new PDE or flow case is one new file, not a fork of the stepper.

Reproducibility

• Bit-exact within a backend: the CPU path reproduces the production solver to the last bit (tested, tests/test_regression_bitexact.py); the GPU path with --rng legacy-cupy reproduces the published dataset seed-for-seed (verify with benchmarks/bench_gpu_cluster.py --paper-npy ...).
• Identical initial data across backends (portable RNG, default).
• Pathwise CPU/GPU bit-equality at t = 0.0035 is not claimed: reductions and transcendentals differ by ULPs between backends and the flow is chaotic; the benchmark reports the divergence growth instead.

Reproducing the paper dataset

cd examples/mach2000_jet
./jobs.sh gen-full                # 20-node GPU array, --rng legacy-cupy, writes $DATA_FULL
./jobs.sh merge --after <jobid>   # merge the part files into samples_{Nx}.npy

The analysis stages read the dataset from DATA_NATIVE. To analyse the regenerated data, set DATA_NATIVE to the same directory as DATA_FULL in acropora-env.sh; to analyse the published dataset instead, point it there. The two are kept separate so a regeneration never overwrites existing data.

The Zenodo record (10.5281/zenodo.23415318) holds the ensembles restricted to the coarsest grid, the convergence and centerline results, and the generation records. To rerun the convergence study without the GPU generation, rebuild the ensemble files there with bash merge_parts.sh, set DATA_ON500 to that folder in acropora-env.sh, and run ./jobs.sh main, ./jobs.sh w2-reference and ./jobs.sh w2-cauchy.

Post-processing (acropora.post, pip install acropora[post]) reproduces the paper's quantities: both comparison protocols (Cauchy: consecutive pairs; reference: each vs the finest grid) with selectable restriction (coarsest, the default and published methodology: every field is block-averaged to the coarsest grid, so all comparisons are evaluated there; pairwise: only the finer field is averaged, onto the coarser member's native grid), the one-point per-cell Wasserstein distance, the two-point Wasserstein distance (POT exact EMD, spatial subsampling), the per-sample strong L1 error, ensemble mean/std L1 errors, log-log rate fits, the centerline percentile bands and one-point density grids, the log-scale PDF heatmaps (rasterized to PNG with the matching \addplot graphics code emitted), and the quantile-band diagnostics behind the statements about those figures. Golden tests assert value-identical output against the reference analysis script in baseline/.

Resolutions are the x-resolutions Nx -- arguments, file names, and CSV columns -- matching the data files: the jet ladder is --resolutions 500 1000 2000 4000, producing samples_500.npy ... samples_4000.npy, centerline_nx500_... ... centerline_nx4000_..., and coarse_nx / fine_nx / compare_nx columns. The transverse count and mesh width follow from the domain via grid_from_nx (Nx=500 -> 500x400, dx=5e-3).

Batch jobs

Batch jobs are submitted through one driver that reads a site file:

cp acropora-env.example.sh acropora-env.sh     # at the repository root, git-ignored
$EDITOR acropora-env.sh                      # venv, partitions, account, data paths
cd examples/mach2000_jet
./jobs.sh restrict                         # once: restrict onto the coarsest grid
./jobs.sh main --after <jobid>             # convergence study (chained)
./jobs.sh w2-reference; ./jobs.sh w2-cauchy
./jobs.sh centerline                       # reads the native data
./jobs.sh verify-gpu                       # GPU bit-exactness vs the dataset
./jobs.sh gen-test                         # small regeneration on one GPU node

./jobs.sh <stage> --dry-run prints the resolved paths and the exact sbatch command without submitting. Nothing has to be exported in the shell: the jobs load the site file themselves, so a fresh login cannot break them.

Funding

Funded by the Federal Ministry of Research, Technology and Space (BMFTR) through the PRIME programme of the German Academic Exchange Service (DAAD). Responsibility for the content of this publication lies with the author.

Citing

If you use acropora, please cite the companion paper (see CITATION.cff, which GitHub and Zenodo parse automatically):

S. Simonis and G. Wissocq,
Computing statistical solutions of a Mach 2000 astrophysical jet,
arXiv:2605.25282 (2026).
https://doi.org/10.48550/arXiv.2605.25282

License

BSD-2-Clause-Patent (BSD 2-clause license with an explicit patent grant). Copyright 2026 Stephan Simonis. Full text in LICENSE.

The acropora logo is © 2026 Stephan Simonis and is not covered by the BSD-2-Clause-Patent license.