SubstrateCommons/canonical-pores

Canonical Pores — Monte-Carlo Replay Packs

Converged Monte-Carlo diffusion walks in the three geometries that have exact analytical solutions — parallel planes, cylinders, spheres — frozen so that any acquisition can be computed afterwards without re-simulating.

600 substrates: 200 diameters per shape, 0.1–20.0 µm in 0.1 µm steps, each walked to T = 200 ms at D₀ = 2.0×10⁻⁹ m²/s. One .rpk (safetensors) per substrate.

What you can replay

A replay pack is not a lookup table of pre-computed signals. It stores the walk itself, so the forward model is evaluated at read time:

you supply	how it is handled	exact?
any gradient waveform G(t) — PGSE, OGSE, PGSTE, CPMG-with-gradients, b-tensor (STE/PTE), arbitrary	projected onto the pack's temporal basis; the gradient phase is linear in position, so Parseval applies	exact for waveform content within the stored bands
surface relaxivity ρ, any value	the pack's boundary-local-time channel, replayed	exact — not a mean-field exp(-TE·ρ·S/V) tag-on
per-compartment T₁ / T₂	compartment map + relaxation log-weights	exact
any b-value, Δ, δ, direction, orientation	consequences of the waveform above	—

There is no short-pulse (SGP) and no Gaussian-phase approximation anywhere in that path. That is the point of the dataset: the analytical models (P2–P5, C2–C5, S2–S5 in dmipy-fit) each hold under some acquisition assumption; replay holds for the acquisition you actually ran.

Not in these packs: susceptibility / off-resonance (no field channel), magnetization transfer, and diffusivity is fixed per pack — D₀ is baked into the walk, not a replay knob. (Time-rescaling to a different D₀ is a planned extension.)

What has been certified, and what that does not mean

Every substrate's replay was compared against the exact eigenmode (matrix-method) solution and sized until the worst residual met ε = 5×10⁻³, measured over a battery of PGSE acquisitions: (δ, Δ) ∈ {(10,20), (10,40), (10,60), (10,100), (5,40)} ms × b ∈ {1, 3, 5}×10⁹ s/m², plus a surface-relaxivity battery. Walker counts were measured, never extrapolated: each candidate count was replayed and compared to the analytic reference on up to five disjoint blocks, all of which had to pass.

That battery is where the bound was measured — it is not a limit on what the pack replays. The distinction matters in one direction only: a waveform whose temporal content falls outside the tested spectral range (very high-frequency OGSE, pulses shorter than the save grid) is still replayable, but its error is not covered by the quoted ε. For these three geometries you can settle that yourself — the exact analytical model ships in dmipy-fit (P5PlaneMatrixMethod, C5CylinderMatrixMethod, S5SphereMatrixMethod), so any acquisition you care about can be checked directly against ground truth. That is precisely what makes this dataset the validity proof for replay on substrates where no analytic answer exists.

Practical resolution limits: the save grid is n_t ∈ {2000, 4000, 8000} over 200 ms, so features finer than that grid are not resolved; and the position codec keeps K ∈ {128, 196} temporal bands, which bounds the waveform bandwidth represented.

shape	substrates	all meet ε=5e-3	worst residual
plane	200	✅	see manifest.json
cylinder	200	✅	see manifest.json
sphere	200	✅	see manifest.json

Each pack carries its own certification in metadata (grid.worst_residual, grid.ladder), so no consumer has to trust this table.

Tiers: fetch only what you need

Two independent selections, and they compose into a single contiguous byte range — verified against HuggingFace range requests (Accept-Ranges: bytes, HTTP 206).

1. Precision (walkers). Walkers are the leading axis of every per-walker tensor, and any prefix is an unbiased sub-ensemble with floor ∝ 1/√n. Each pack ships the measured prefix length for each floor:

grid["prefix_tiers"]   # e.g. {"0.03": 1000, "0.02": 1000, "0.01": 1000, "0.005": 1000}

2. Spatial axis. Positions are stored as one tensor per axis (pos_x, pos_y, pos_z, each (n_walkers, K)), so you fetch only the components your geometry needs — a slab restricts one direction (the other two are free and analytic), a cylinder two, a sphere three. All three are always present, so rotating / b-tensor encodings that need the joint trajectory lose nothing.

Measured on a 17.36 MiB pack: one axis + a 2,000-walker prefix = 0.49 MiB, a 36× reduction.

from safetensors import safe_open
with safe_open("cylinder/d10.00um.rpk", framework="np") as f:
    x = f.get_slice("pos_x")[0:2000]        # one axis, coarse tier: one contiguous read

Status of the two selections. Both are real and verified at the byte level, but only one is automatic today:

• Per-diameter fetch is automatic. The X6 compartments resolve a fitted diameter to the two bracketing packs and download only those, so a fit transfers ~tens of MiB, never the dataset.
• Coarser-ε prefix fetch is automatic too, via eps=:

from dmipy_fit.data.mc_replay import load_replay_family
fam = load_replay_family("cylinder", 2e-9, eps=1e-2)   # range-reads each pack down to its 1e-2 tier

Measured live on this dataset (cylinder d=13.45 µm, 50,000-row pack): ε=5e-3 moves 43.39 MiB, ε=1e-2 moves 17.36 MiB, ε=3e-2 moves 4.34 MiB — a 10× reduction — with the delivered accuracy tracking the request. The tier count comes from manifest.json, so choosing one costs no transfer, and an ε with no measured tier raises rather than silently returning something coarser.

axes= restricts which position components are fetched (1 for a slab, 2 for a cylinder's transverse plane) for a further 1.5–3×. It is not defaulted: rotating / b-tensor encodings need the joint trajectory, so ask for it only when your encoding is fixed-direction.

Usage

from dmipy_sim import read_rpk, compile_scheme, replay_signal
pack = read_rpk("cylinder/d05.00um.rpk")
W = compile_scheme(G, dt, pack.meta["compression"]["K"])   # G: (n_meas, n_t, 3), any waveform
E = replay_signal(pack, W)                                  # + rho_over_D= for surface relaxivity

As fit compartments (X6), with the same parameters as their analytic siblings:

from dmipy_fit.signal_models.cylinder_models import C6MonteCarloReplayCylinder
model = C6MonteCarloReplayCylinder()        # mu, lambda_par, diameter — fetches packs on demand

manifest.json lists every substrate with its walker count, size, certified residual and prefix tiers.

Layout

canonical/D0-2.00e-9/{plane,cylinder,sphere}/d<NN.NN>um.rpk
manifest.json

Citation

Generated with dmipy-sim. Please cite the dataset DOI and the dmipy-sim replay-pack reference. CC-BY-4.0.