SANDIX: Granular Materials & MRI Models

• The paper on granular materials demonstrates a two-stage SANDIX framework that autoencodes 3D sand grain point clouds and employs a latent-space denoising diffusion model to generate grains with high morphological fidelity.
• The paper on diffusion MRI introduces SANDIX as a six-parameter biophysical model incorporating a soma compartment to traditional neurite–extracellular exchange, though several parameters show high uncertainty.
• SANDIX is a disambiguated term applied in distinct domains, making precise citation and context essential to distinguish it from similarly named methods in feature matching and detector physics.

Searching arXiv for “SANDIX” to ground the article in current preprints and verify the term’s usage. SANDIX is a term that appears in more than one technical context in the provided arXiv record. In granular-materials research, it denotes a latent-space denoising diffusion pipeline for synthesizing realistic sand grains from three-dimensional scans and then constructing granular assemblies with targeted distributional properties (Vlassis et al., 2023). In diffusion MRI, it denotes Soma and Neurite Density Imaging with EXchange, a six-parameter gray-matter biophysical model that combines neurite–extracellular exchange with a restricted soma compartment and has been studied through Bayesian uncertainty quantification (Jallais et al., 26 Aug 2025). The same string also appears as a source of terminological confusion with unrelated methods and systems, including SANDesc, SANDD, and the Granule-in-Cell method (D'Urso et al., 19 Jan 2026, Li et al., 2019, Sutanto et al., 2021, Tang et al., 1 Apr 2025).

1. Term usage and domain scope

The two principal uses of SANDIX in the supplied literature differ in both subject matter and mathematical structure. One concerns generative modeling of particulate morphology; the other concerns compartmental signal modeling in diffusion MRI. Several neighboring papers explicitly indicate that SANDIX is not their method name, which makes disambiguation necessary in technical writing and indexing (Vlassis et al., 2023, Jallais et al., 26 Aug 2025, D'Urso et al., 19 Jan 2026, Li et al., 2019, Sutanto et al., 2021, Tang et al., 1 Apr 2025).

Usage	Domain	Definition
SANDIX	Granular materials	Latent-space diffusion pipeline for synthetic sand grains and assemblies
SANDIX	Diffusion MRI	Soma and Neurite Density Imaging with EXchange
SANDesc	Local feature matching	Descriptor architecture; “SANDIX” is a mistaken variant
SANDD	Antineutrino detection	Segmented AntiNeutrino Directional Detector
GIC	Sand–water simulation	Granule-in-Cell method; no SANDIX acronym is defined

This terminological split has practical consequences. In the granular-materials paper, SANDIX is a generative framework whose outputs are synthetic point clouds and derived assemblies. In the dMRI paper, SANDIX is a forward signal model whose outputs are fitted microstructural parameters and associated posterior uncertainties. Conflating these usages obscures both implementation assumptions and evaluation criteria.

2. SANDIX as a latent-diffusion framework for synthetic sand

In the sand-generation setting, SANDIX is a two-stage generative pipeline trained on synchrotron microcomputed tomography scans of F50 silica sand. Its purpose is to avoid hand-crafted grain-shape descriptors and instead learn a data-driven distribution directly from real three-dimensional grain geometries. The training data are surface-derived point clouds from individual grains, represented as

$P=\{p_1,p_2,\dots,p_N\}\subset \mathbb{R}^3,$

with each point $p_i=(x_i,y_i,z_i)$. Most grains have 600 vertices, and only grains with that count are retained, leaving 1,542 real grains for diffusion training. Each point is augmented with 8 additional features from a node2vec embedding of the undirected mesh connectivity graph, so the autoencoder input has 11 dimensions per point: 3 Cartesian coordinates plus 8 learned adjacency/topology features (Vlassis et al., 2023).

The representation-learning stage is a 1D convolutional point-cloud autoencoder. Its encoder maps the 11-feature point cloud through a 1D convolution from 11 channels to 64, followed by PReLU, then another 1D convolution from 64 to 784 channels, again with PReLU. An AdaptiveMaxPool1d layer compresses the feature map into a $28\times 28$ latent representation. The decoder applies a 1D convolution from 784 to 64, a PReLU, and a final 1D convolution producing 1800 outputs, reshaped into $(600,3)$. Reconstruction is optimized with the Chamfer distance, chosen because it is permutation-invariant and does not require point-to-point correspondence. Training uses Adam with learning rate $10^{-3}$, batch size 16, 1000 epochs, and a ReduceLROnPlateau scheduler.

After autoencoding, SANDIX trains a denoising diffusion probabilistic model in latent space. The forward process corrupts a latent sample $x_0$ by Gaussian noise over $T$ steps according to

$$q(x_t\mid x_{t-1})=\mathcal{N}(x_t;\sqrt{1-\beta_t}\,x_{t-1},\beta_t I).$$

The reverse process is parameterized by a U-Net, and training uses a hybrid objective consisting of a noise-prediction term and a variational lower-bound term,

$$L_{\text{hybrid}} = L_\mu + \lambda L_{\text{vlb}},$$

with $\lambda=0.001$. Sampling begins from Gaussian noise in latent space, applies the learned reverse transitions, and decodes the resulting latent code to a synthetic grain point cloud. This latent-space construction is significant because the diffusion model operates on a compact embedding rather than directly on high-dimensional geometric data.

3. Morphological fidelity, meshing, and assembly synthesis

The granular SANDIX pipeline is validated at three levels: reconstruction fidelity, generative fidelity, and assembly-level plausibility. The authors report that the autoencoder reconstructs test grains well, with only slight smoothing of sharp edges. The diffusion model generates grains whose morphology, shape, and size are consistent with the F50 database. When 1,536 grains are sampled, the generated size distribution remains entirely within the database range. When 50,000 grains are generated, only 58 grains, or 0.116%, fall outside the original size range. Reported $p_i=(x_i,y_i,z_i)$0, $p_i=(x_i,y_i,z_i)$1, $p_i=(x_i,y_i,z_i)$2, coefficient of uniformity $p_i=(x_i,y_i,z_i)$3, and coefficient of curvature $p_i=(x_i,y_i,z_i)$4 for the synthetic sets closely match the real database, as do the mean, median, standard deviation, and extreme diameters. Shape statistics derived from the surface orientation tensor—compactness $p_i=(x_i,y_i,z_i)$5, flakiness $p_i=(x_i,y_i,z_i)$6, and elongation $p_i=(x_i,y_i,z_i)$7—also track the database distributions, although some rare database outliers are not fully recovered (Vlassis et al., 2023).

For assembly synthesis, point clouds are meshed in PyMeshLab; normals are estimated from 5 nearest neighbors; and the ball-pivoting algorithm reconstructs triangular surfaces. The rigid grains are then deposited under gravity in Blender’s physics engine inside a cylindrical container 2.5 mm tall and 1.4 mm in diameter. Grains are placed randomly above the container at heights between 7 and 14 mm until a static equilibrium packing is obtained. In one comparison, 209 real grains and 237 generated grains were needed to fill the same container height, and the resulting assemblies showed similar cross-sectional structure and similar contact-network descriptors, including porosity, coordination number, transitivity, graph density, and local efficiency.

A distinctive feature is targeted assembly synthesis. Because SANDIX can generate grains in bulk, the authors subsample from 50,000 synthetic grains according to prescribed size or shape ranges before deposition. Three size-targeted ranges—small grains (A), medium grains (B), and large grains (C)—and three shape-targeted ranges—(D, E, F) in the $p_i=(x_i,y_i,z_i)$8-$p_i=(x_i,y_i,z_i)$9-$28\times 28$0 ternary space—are demonstrated. Smaller grains yield more particles in the container, lower porosity, and higher coordination number; larger grains yield fewer particles, higher porosity, and lower connectivity. This suggests that SANDIX functions not only as an unconditional generator of grain morphology but also as a mechanism for constructing assemblies with prescribed distributional properties.

4. SANDIX as a gray-matter diffusion MRI model

In diffusion MRI, SANDIX stands for Soma and Neurite Density Imaging with EXchange. It is a gray-matter biophysical model designed to capture both permeative water exchange between neurites and extracellular space and restricted diffusion inside somas. It is positioned relative to three earlier models: NEXI, a two-compartment exchange model with neurites and extracellular space but no soma compartment; SMEX, which generalizes exchange modeling to arbitrary gradient waveforms; and SANDI, which includes a soma compartment but not exchange in the same way as SANDIX. In this construction, SANDIX adds a soma compartment to the exchange formalism, increasing biological scope while also increasing fitting complexity (Jallais et al., 26 Aug 2025).

SANDIX estimates six parameters:

$28\times 28$1 (exchange time between neurites and extracellular space), $28\times 28$2 (intra-neurite diffusivity), $28\times 28$3 (extra-neurite diffusivity), $28\times 28$4 (absolute neurite signal fraction), $28\times 28$5 (soma radius), and $28\times 28$6 (soma signal fraction). The absolute neurite fraction is defined as

$28\times 28$7

Its full direction-averaged signal is

$28\times 28$8

with fixed soma diffusivity

$28\times 28$9

The soma compartment is modeled as impermeable spheres under the Gaussian Phase Approximation, and the paper explicitly states that soma exchange with neurites or extracellular space is neglected at diffusion times below 20 ms.

This formulation makes SANDIX a composite model: the neurite–extracellular subsystem inherits the exchange dynamics of SMEX/NEXI, while the soma term contributes a restricted spherical signal. A plausible implication is that SANDIX gains descriptive richness by superposing mechanisms that are individually motivated but only partially identifiable under realistic acquisition constraints.

5. Bayesian inference, acquisition protocols, and parameter identifiability

The uncertainty analysis of SANDIX in diffusion MRI is built around µGUIDE, a simulation-based Bayesian inference framework with two jointly optimized components: an MLP encoder for dimensionality reduction and a Neural Posterior Estimator implemented with masked autoregressive flow normalizing flows. The network is trained to minimize KL divergence between the true and approximate posterior. For each voxel, inference returns a MAP estimate, an uncertainty measure defined as the interquartile range of the 50% most probable posterior samples, and a degeneracy flag when the posterior is multimodal. Training uses $(600,3)$0 simulations per condition, 5% validation, learning rate $(600,3)$1, batch size 128, early stopping after 50 epochs, fine-tuning at $(600,3)$2, and 50,000 posterior samples at inference time (Jallais et al., 26 Aug 2025).

Two acquisition protocols are compared. The extensive ex vivo protocol uses a 16.4 T Bruker Aeon scanner with gradient strength up to 3000 mT/m, $(600,3)$3 ms, and $(600,3)$4 ms. The in vivo NEXI 3T Connectom protocol uses a 3T Siemens Connectom, 300 mT/m gradient amplitude, b-values 1, 2.5, 4, 6, 7.5 ms/µm², diffusion times $(600,3)$5 ms, $(600,3)$6 ms, and total scan time 45 minutes. Simulations add Rician noise with median SNR ≈ 50, and in vivo fitting is performed on data from 4 healthy volunteers, with 2 rescanned on another day.

The main empirical result is a strong asymmetry in parameter robustness. Across simulations and in vivo data, $(600,3)$7 and $(600,3)$8 are the most robust SANDIX parameters. By contrast, $(600,3)$9, $10^{-3}$0, $10^{-3}$1, and $10^{-3}$2 exhibit high uncertainty, bias, degeneracies, or protocol dependence. For SANDIX on Connectom + noise, the paper states that exchange time estimates are mostly unreliable, that $10^{-3}$3 and $10^{-3}$4 remain robust, that soma radius uncertainty rises for $10^{-3}$5, and that soma fraction $10^{-3}$6 is highly uncertain across the explored range. In vivo, $10^{-3}$7 is reliable only for a tiny fraction of voxels, and $10^{-3}$8 is even less stable.

Parameter	Degenerate voxels	Voxels with <10% uncertainty
$10^{-3}$9	0.45%	26.73%
$x_0$0	0.02%	11.80%
$x_0$1	0.29%	85.37%
$x_0$2	0.04%	44.96%
$x_0$3	0.15%	3.45%
$x_0$4	0.24%	0.06%

These numbers formalize a central interpretive constraint: point estimates alone are insufficient for SANDIX. The paper also reports that noise increases bias and uncertainty and can hide degeneracies by broadening posteriors until multiple modes merge into a single wider mode. Compared with non-linear least squares, µGUIDE is reported to be faster on simulations by about 5–12×, while additionally providing uncertainty quantification, degeneracy detection, and filtering of unreliable estimates.

6. Neighboring methods and recurrent confusions

Several supplied papers explicitly distinguish their own method names from SANDIX, which makes the term unusually prone to cross-domain misidentification. In local feature matching, the method introduced in “A Streamlined Attention-Based Network for Descriptor Extraction” is SANDesc, not SANDIX. SANDesc is a descriptor extraction architecture with a revised U-Net-like network, Convolutional Block Attention Modules, Residual U-Net Blocks with Attention, a modified triplet loss, and a curriculum learning-inspired hard negative mining strategy; its separate benchmark contribution is Graz4K (D'Urso et al., 19 Jan 2026). In this setting, “SANDIX” is described as a mistaken variant or misspelling of SANDesc.

In detector physics, SANDD denotes Segmented AntiNeutrino Directional Detector, not SANDIX. The 2019 prototype paper studies an $x_0$5 array of pulse-shape-sensitive plastic scintillator rods read out by two 64-channel SiPM arrays, demonstrating neutron/gamma pulse-shape sensitivity, multiplicity-based particle identification, and approximately 1 cm longitudinal position resolution at 1 MeVee (Li et al., 2019). The 2021 detector paper describes a 9-liter, 0.1 wt% $x_0$6Li-doped plastic-scintillator system for near-field reactor monitoring, with predicted 20.0% $x_0$7 (stat.) $x_0$8 (syst.) inverse beta decay detection efficiency and an azimuthal directional uncertainty of about $x_0$9 for 100 detected antineutrino events (Sutanto et al., 2021). Neither paper defines SANDIX.

In sand–water simulation, the proposed method is Granule-in-Cell (GIC), a hybrid DEM + PIC framework with bidirectional coupling, volume-fraction projection, implicit density projection, wetting by phase transfer from fluid particles to DEM granules, and concentration-gradient or capillary effects. The paper explicitly states that SANDIX is not explicitly defined there as a named acronym (Tang et al., 1 Apr 2025). Taken together, these cases show that the string “SANDIX” functions both as a legitimate method name in some domains and as a recurrent transcription error in others, so precise expansion and citation are essential.

7. Significance of the term across research areas

The two genuine SANDIX usages illustrate markedly different conceptions of modeling. In granular materials, SANDIX is a generative framework: it learns a latent distribution over grain morphologies from 1,542 real SMT scans, generates synthetic grains at scale, and supports assembly construction with controllable size and shape statistics (Vlassis et al., 2023). In diffusion MRI, SANDIX is a mechanistic signal model: it parameterizes gray-matter microstructure through exchange and restriction, and its main methodological challenge is identifiability under realistic acquisition and noise constraints (Jallais et al., 26 Aug 2025).

This contrast is scientifically instructive. The sand-generation SANDIX succeeds by approximating a complex empirical distribution without hand-engineered descriptors; the dMRI SANDIX seeks biophysical interpretability but encounters posterior broadening, bias, and multimodality for several parameters. A plausible implication is that the same label now spans both synthesis and inference paradigms, and therefore acquires meaning only through its domain-specific expansion, equations, and evaluation methodology. In bibliographic and technical contexts, “SANDIX” is best treated not as a single unified concept, but as a disambiguated term whose referent must be specified by field and citation.