maxwellgp

A Gaussian process (GP) framework for modeling 3D time-harmonic electromagnetic fields constrained by Maxwell's equations, built on JAX. The prior is an Ehrenpreis-Palamodov plane-wave feature map, so every sample and the posterior mean satisfy the homogeneous Maxwell system exactly; only the data (boundary or interior field observations) are fit.

This is the general-purpose solver core. The cavity-specific physics and the reaction-operator assembly live in cavity-epgp, which depends on this package.

Public API

• MaxwellKernel(n_spectral, wavenumber, trace=..., key=...) plane-wave feature map; trace="tangential" conditions on the tangential trace.
• GaussianProcess(kernel, log_noise=...) the regression core: marginal likelihood (nlml) and condition(X, Y).
• GaussianProcessPosterior posterior mean, cov, var given feature evaluations.

A field point is a 3-vector; conditioning points carry a normal (a 6-vector, position and normal stacked). The model predicts the 6-vector field [E, B].

Requirements

• uv

Example

uv run python examples/basic.py

examples/basic.py fits a known plane-wave superposition from sampled points and reports the recovered-field RMSE, exercising the kernel, marginal-likelihood training, and posterior mean.

Development

uv run ruff check
uv run pyright