nornax

nornax is a JAX-native Hermite integrator package for gravitational N-body dynamics.

The current direction is:

• standalone and general-purpose first
• Diffrax-facing solver design
• GPU-efficient JAX kernels
• clean backend adapters so jaccpot can plug in later

Current Scope

The current implementation includes:

• immutable NBodyState / ForceDerivatives PyTrees
• backend-agnostic ForceModel protocol
• standalone DirectSumGravity reference backend (O(N^2) all-pairs; the default path materializes N×N pair tensors, and an opt-in block_size caps peak memory at O(block_size × N) for larger N — jaccpot remains the scalable backend)
• standalone and Diffrax-backed Hermite-4, Hermite-6, and Hermite-8
• adaptive global timestep control through Diffrax
• diagnostics for total energy and angular momentum
• convergence and long-run conservation tests

Installation

Install from source:

pip install -e .

Install with development tooling:

pip install -e ".[dev]"

Quick Start

import jax
import jax.numpy as jnp

from nornax import AarsethController, solve_adaptive_to_time, total_energy
from nornax.forces import DirectSumGravity

jax.config.update("jax_enable_x64", True)

force_model = DirectSumGravity()
result = solve_adaptive_to_time(
    jnp.asarray([[-1.0, 0.0, 0.0], [1.0, 0.0, 0.0]]),
    jnp.asarray([[0.0, 0.5, 0.0], [0.0, -0.5, 0.0]]),
    jnp.asarray([1.0, 1.0]),
    force_model,
    t_final=1.0,
    order=8,
    controller=AarsethController(eta=0.03, min_dt=1.0e-4, max_dt=5.0e-2),
    atol=1.0e-8,
)
print(result.final_state.time, total_energy(result.final_state))

Examples:

• examples/two_body_diffrax.py: adaptive two-body solve
• examples/compare_hermite_orders.py: compare Hermite-4/6/8 energy and angular-momentum drift
• examples/plummer_sphere_gpu.py: small Plummer sphere run shaped for GPU/server use

Notebooks:

• notebooks/hermite_orders_accuracy.ipynb: compare adaptive Hermite-4/6/8 drift and step counts
• notebooks/hermite_vs_diffrax_rk.ipynb: compare Hermite against a standard Diffrax RK solver
• notebooks/direct_vs_jaccpot_backend.ipynb: compare direct-sum and jaccpot backends for Hermite-4
• notebooks/plummer_sphere_gpu.ipynb: small Plummer sphere application notebook for GPU/server runs

Jaccpot Adapter

nornax now includes a first adapter for jaccpot via JaccpotForceModel. This is useful today for Hermite-4, because the current jaccpot runtime exposes acceleration and jerk, but not higher time derivatives.

import jax.numpy as jnp

from jaccpot import FastMultipoleMethod
from nornax import AarsethController, JaccpotForceModel, solve_adaptive_to_time

solver = FastMultipoleMethod(preset="fast", basis="solidfmm")
force_model = JaccpotForceModel(solver)

result = solve_adaptive_to_time(
    jnp.asarray([[1.0, 0.0, 0.0], [-1.0, 0.0, 0.0]]),
    jnp.asarray([[0.0, 0.2, 0.0], [0.0, -0.2, 0.0]]),
    jnp.asarray([1.0, 1.0]),
    force_model,
    t_final=0.1,
    order=4,
    controller=AarsethController(eta=0.03, min_dt=1.0e-4, max_dt=5.0e-2),
    atol=1.0e-6,
    args={"leaf_size": 8, "max_order": 2, "jerk_mode": "fast_approx"},
)

Current limitation:

• use JaccpotForceModel with Hermite-4 for now
• Hermite-6 and Hermite-8 still require higher time derivatives than jaccpot currently provides

Planned Architecture

• nornax.state: particle state and cached force derivatives
• nornax.forces: standalone direct-sum backend plus future adapters
• nornax.solvers: Hermite kernels and Diffrax-facing solver classes
• nornax.terms: thin Diffrax integration hooks

The scientific target is the family of higher-order Hermite methods discussed by Nitadori, Iwasawa, and Makino. The current implementation follows that paper through Hermite-8, including direct derivatives through crackle and higher-order adaptive timestep criteria.

Validation

The test suite currently covers:

• direct-force derivatives through crackle
• Hermite-4/6/8 kernel behavior
• Diffrax custom solver smoke tests for 4/6/8
• convergence checks for 4/6/8
• adaptive public solve APIs
• long-run two-body energy-drift ordering across 4/6/8

Benchmarks and examples live in bench/bench_direct_sum.py and examples/compare_hermite_orders.py.

Development

Run quality gates locally:

black --check .
isort --check-only .
pytest

Or run pre-commit hooks:

pre-commit run --all-files

Runtime Type Checking

Enable package-wide runtime checks (jaxtyping + beartype) at import time:

export NORNAX_RUNTIME_TYPECHECK=1

License

MIT.