magpylib-jax 2.1.0

Differentiable JAX-native magnetic field modeling with Magpylib-compatible APIs

magpylib_jax

Analytic magnetic fields that you can differentiate, compile, and optimize through.

magpylib_jax is a clean-room, JAX-native reimplementation of Magpylib. It keeps Magpylib's ergonomic object and functional APIs and its analytic field models, but replaces the numerical core with a differentiable, JIT-compilable, vmap-friendly implementation — so the same field computation you use for analysis can sit inside a jax.grad optimization loop.

Why magpylib_jax?

Magpylib gives you fast closed-form fields but no derivatives. Finite-differencing it through an optimizer is slow and noisy. magpylib_jax closes that gap:

• End-to-end differentiable — jax.grad, jacfwd, jacrev through getB/getH/getJ/getM and through geometry, pose, and excitation. Exact gradients, no finite differences.
• Compiled & vectorized — the field core runs under jax.jit/vmap/XLA on CPU/GPU/TPU.
• Exact force & torque — getFT computes magnetic force and torque by autodiff (∇(m·B)), so — unlike Magpylib's finite-difference getFT — the magnet result is independent of a step size eps and exact to machine precision.
• Magpylib-compatible — same source classes, Collection, Sensor, path/orientation motion, squeeze/pixel_agg semantics, and SI units, validated against upstream in CI.
• Lean & readable — the numerical core is split into small, well-named modules (core/kernels/, fields/) with one obvious way to compute each field.

Differences from Magpylib

	Magpylib 5.x	magpylib_jax
Backend	NumPy	JAX (CPU/GPU/TPU, XLA)
Gradients	✗ (finite-diff by hand)	✓ grad/jacfwd/jacrev, exact
jit / vmap	✗	✓ field core
getFT force/torque	finite differences (step eps)	autodiff, exact, eps-free
Precision	float64	float64 (x64 enabled on import)
3-D show() display	✓ (matplotlib/plotly/pyvista)	✓ (matplotlib)
Source families	all	all 12 (parity-tested)

magpylib_jax matches magpylib's numerical surface and adds exact gradients and getFT. It ships a matplotlib show() (below); the extra plotly/pyvista backends and the full interactive style system are the only display features left aside. See the parity strategy.

Installation

pip install magpylib-jax

For GPU/TPU, install the matching jax/jaxlib build first, then magpylib-jax. Development install:

pip install -e '.[test,docs]'
pytest

Quickstart

import jax, jax.numpy as jnp
import magpylib_jax as mpj                     # enables float64 on import

# Object API — identical feel to magpylib
src = mpj.magnet.Cuboid(polarization=(0, 0, 1.0), dimension=(1.0, 1.0, 1.0))
B = src.getB([(2.0, 0.0, 0.0), (0.0, 0.0, 2.0)])   # tesla, shape (2, 3)

# Differentiate the field w.r.t. any parameter
def bz(height):
    return mpj.magnet.Cuboid(polarization=(0, 0, 1.0),
                             dimension=(1.0, 1.0, height)).getB((2.0, 0, 0))[2]
print(jax.grad(bz)(1.0))                            # dB_z / d(height)

Inverse design in a few lines

Because the field is differentiable, fitting geometry or excitation to a target is just gradient descent — no finite differences, no wrappers:

import jax, jax.numpy as jnp
import magpylib_jax as mpj

obs = jnp.array([[0.2, 0.1, 0.4], [0.5, 0.0, 0.7]])
target = jnp.array([[2.0e-4, 0.0, 3.0e-4], [1.0e-4, 0.0, 2.0e-4]])

def loss(pol):
    pred = mpj.magnet.Cuboid(dimension=(1.0, 0.8, 1.2), polarization=pol).getB(obs)
    return jnp.mean((pred - target) ** 2)

grad = jax.jit(jax.grad(loss))
pol = jnp.array([0.05, -0.02, 0.08])
for _ in range(100):
    pol = pol - 1e-1 * grad(pol)

The plot on the right above shows the loss for recovering a dipole moment this way.

Force & torque by autodiff — getFT

import magpylib_jax as mpj
from magpylib_jax import getFT

magnet = mpj.magnet.Cuboid(polarization=(0, 0, 1.0), dimension=(1., 1., 1.))
loop   = mpj.current.Circle(diameter=2.0, current=1e3, position=(0, 0, 1.0), meshing=50)
F, T = getFT(magnet, loop)          # force (N) and torque (N·m)

Force on a magnet is F = ∇(m·B) obtained with jax.jacfwd, and current force is (I dL)×B. The magnet result carries no finite-difference step, so it is exact and eps-independent — and getFT is itself differentiable.

Performance

The benchmark above is measured on CPU, with the field wrapped in jax.jit and compilation paid once (the intended usage inside an optimization loop):

• Forward field (left): once jitted, magpylib_jax's XLA kernel is competitive with — and here several times faster than — Magpylib's NumPy core on large observer batches. On GPU/TPU the same kernel parallelizes further.
• Field + gradient (right): Magpylib has no autodiff, so a gradient of a field-derived quantity w.r.t. source parameters needs finite differences — 6 extra forward evaluations for a 3-component polarization, and only approximate. magpylib_jax returns the exact gradient from one reverse pass (value_and_grad), roughly an order of magnitude faster here and machine-precise.

Two caveats worth knowing: jax.jit your field function and reuse it (the eager object API pays per-call dispatch overhead that dominates small problems), and for timing wrap results in jax.block_until_ready(...) so you measure compute, not async dispatch. This applies to getFT too — it is jittable and differentiable when the geometry and meshing are static (only the excitation/pose are traced), so jax.jit(jax.grad(loss)) over a getFT-based loss compiles once.

The benchmark is CPU. The panel titles report the active backend, so re-running python scripts/make_figures.py on a GPU/TPU host regenerates the figure with that device's numbers, where the batched, fused kernels parallelize much further.

Visualize with show()

import magpylib_jax as mpj

scene = mpj.Collection(
    mpj.magnet.Cuboid(polarization=(0, 0, 1.0), dimension=(1, 1, 1)),
    mpj.current.Circle(diameter=2.0, current=100.0, position=(1.5, 0, -1)),
    mpj.misc.Dipole(moment=(0, 0, 1.0), position=(1.5, 0, 1)),
    mpj.Sensor(position=(0, 0, -1.2), pixel=[[0, 0, 0]]),
)
scene.show()   # or mpj.show(obj_a, obj_b, ...)

Magnets render as shaded bodies with a polarization arrow, currents as loops/lines with a direction arrow, dipoles as moment arrows, and sensors as markers with their pixel grid and local axes; paths draw as faint trails. Pass an existing ax to compose with your own figure, or return_fig=True for headless use.

Supported sources

magnet.Cuboid, magnet.Cylinder, magnet.CylinderSegment, magnet.Sphere, magnet.Tetrahedron, magnet.TriangularMesh, current.Circle, current.Polyline, current.TriangleSheet, current.TriangleStrip, misc.Dipole, misc.Triangle, misc.CustomSource — plus Collection and Sensor.

Documentation

• Overview · Quickstart
• Equation models & derivations · Numerics & differentiability
• Examples: object API, functional API, force & torque, visualization, optimization, performance
• Architecture & source map · Testing & validation
• Performance · Parity strategy · API reference
• Refactor & roadmap plan · Changelog

Citing

If magpylib_jax supports your research, please cite this repository and the upstream Magpylib papers it builds on (see docs/equations.md for the model references).

License

BSD-2-Clause. Built by the UW-Madison plasma group as a differentiable companion to Magpylib.