jma02/helmholtz-scattering-3d

Free-space 3D Helmholtz multistatic scattering

Synthetic dataset of multistatic far-/near-field scattering matrices for penetrable scatterers in 3D free space, generated with the jaxhps HPS+BIE forward solver (examples/scattering_dataset_3d.py).

Physics

Each sample is a sum of n in {1,2,3} smooth radial bumps

b(x) = sum_k A_k (1 - (|x - c_k|/R_k)^2)^4  for |x - c_k| < R_k,

with squared refractive index n(x)^2 = 1 - b(x). The scattered field solves

Lap u^s + kappa^2 (1 - b) u^s = kappa^2 b u^inc,   u^inc = exp(i kappa w . x),

with the Sommerfeld radiation condition (kappa = 4.0).

Geometry

• Cube half-width a = 1.25 (HPS domain [-a, a]^3), boundary order q = 8, octree depth L = 2, interior Chebyshev order p = 12.
• 128 plane-wave transmitter directions (Fibonacci sphere).
• 128 receivers on a sphere of radius rho = 2.5 (Fibonacci sphere).
• Scatterer support is constrained to |c_k| + R_k <= 1.1.

The exact transmitter directions and receiver points are in metadata.json (tx_dirs, rx_pts).

Fields

column	shape	description
n_scatterers	scalar	number of bumps (1-3)
centers	3x3 (flattened, NaN-padded)	bump centers c_k
radii	3 (NaN-padded)	bump radii R_k
amps	3 (NaN-padded)	bump amplitudes A_k
u_real, u_imag	128*128 (flattened)	Re/Im of M[j_rx, i_tx]
sample_index	scalar	deterministic seed index

Loading

import json
import numpy as np
from datasets import load_dataset

ds = load_dataset("jma02/helmholtz-scattering-3d", split="train")
meta = json.load(open("metadata.json"))  # or hf_hub_download
nrx, ntx = meta["matrix_shape"]

ex = ds[0]
M = (np.array(ex["u_real"]) + 1j * np.array(ex["u_imag"])).reshape(nrx, ntx)
centers = np.array(ex["centers"]).reshape(meta["n_scatterers_max"], 3)

Generated by jaxhps.