GeoDict Generate Granular Twin GeoApp

The Generate Granular Twin GeoApp is an automated statistical digital twin tool developed by GeoDict for granular materials. It can start from 2D SEM images, material thin sections, CT slices, or complete 3D scan data to generate new 3D granular microstructures, and through an optimization process, makes their geometric statistics and selected physical properties as close as possible to the reference material.

With this GeoApp, users can automatically build digital twins of granular materials from 2D or 3D images, combine grain packing with Gaussian or Laplacian random fields, match pore size, grain size, chord length, and specific surface area, and further match permeability and diffusivity in 3D mode. The tool automatically optimizes grain size, random field, and binder parameters, creates multiple statistically equivalent but locally different digital samples, reconstructs materials at different resolutions and volumes, and uses the final model for flow, diffusion, and other property simulations.

What Is a Statistical Digital Twin of Granular Materials?

The "digital twin" here is not a voxel‑by‑voxel copy of the reference image. Instead, based on statistical information extracted from the reference structure, it generates a new random 3D structure that matches the original material as closely as possible in the metrics of interest.

Metrics that can be matched include grain size distribution, pore size distribution, solid phase size distribution, chord length distribution, specific surface area, porosimetry results, permeability, diffusivity, and structural features related to transport paths. Therefore, twins generated with different random seeds can have different local grain arrangements but remain similar in target statistics and effective properties. This allows users to construct multiple statistically equivalent digital samples from a single reference image of limited size.

Two Working Modes

The Generate Granular Twin GeoApp supports two basic working modes. The Generate Granular Twin From 2D mode uses SEM images, thin sections, or 2D slices from 3D scans as reference data, and is primarily used to generate statistically consistent 3D microstructures from limited 2D information. The Generate Granular Twin From 3D mode uses segmented CT, FIB‑SEM, or other 3D structures as reference, and is used to generate new models matching the statistics and properties of the original 3D structure. Math2Market emphasizes its 2D‑to‑3D capability: even with only 2D thin sections or SEM images, 3D geometries can be generated, and 3D properties such as permeability can be further predicted.

Automated Generation and Optimization Workflow

The GeoApp provides a complete automated workflow: import 2D or 3D reference structure, analyze geometric and physical properties of the reference, set twin generation method and target metrics, generate initial grain structure, compute grain distance field and random field, threshold to form solid and pore phases, compute twin target properties, compare with reference and calculate error, automatically adjust structure generation parameters, iterate until stopping condition is met, and output optimized 3D statistical digital twin.

In each optimization iteration, the GeoApp generates a new candidate structure, analyzes its properties, and compares them with reference values. The error function is used to comprehensively represent deviations in each target metric, and the optimizer adjusts parameters such as grain size, random field, overlay strength, or binder proportion accordingly.

Modeling Approach: Grain Packing Combined with Random Fields

The GeoApp is not limited to ideal spherical grains. It combines a grain generator, distance field, and random field thresholding to generate irregular grain morphologies closer to real materials. A single structure generation consists of three main steps: grain packing or grain structure generation, distance field computation, and thresholding using up to two Gaussian random fields. By adjusting the overlay strength between the grain structure and the random field, users can control the appearance from "distinct discrete grain morphology" to "continuous, irregular random solid phase morphology."

Grain Generator – The GeoApp can call GrainGeo's grain generation capabilities, allowing selection of basic grain shapes including sphere, ellipsoid, convex polyhedron, or using only the random field to generate the structure.

Gaussian or Laplacian Random Field – Users can choose no random field, one isotropic random field, or two isotropic random fields. Available correlation functions include Isotropic Squared Exponential (Gaussian) and Isotropic Exponential (Laplacian).

Grain–Random Field Overlay – The overlay strength controls the relative contribution of the grain structure and the random field to the final structure. At 100%, the structure is completely determined by grain packing; at 0%, it is completely determined by the random field; in between, it blends grain geometry with random field morphology.

Adding Binder Regions – The GeoApp can also call GrainGeo's Add Binder function, filling some small pores between grains with the same solid material, creating a more connected solid network. Users control the filling amount via Binder Solid Volume Percentage.

Selectable Matching Targets

For 2D reference structures, optional metrics include pore and solid granulometry, pore and solid chord length distribution, specific surface area, and out‑of‑plane 2D permeability. For 3D reference structures, more complete 3D comparisons are supported, including pore and solid granulometry, porosimetry (pore throat size distribution), pore and solid chord length, specific surface area, permeability in specified directions (requires FlowDict), and diffusivity in specified directions (requires DiffuDict). Users can select one or more metrics and combine them into the optimization error function.

Structural Parameters That Can Be Automatically Adjusted

Users can choose to let the optimizer adjust one or more of the following parameter groups: overlay strength between grain structure and random field, mean grain diameter, grain diameter standard deviation, aspect ratio (for ellipsoids or convex polyhedra), random field correlation length, relative influence of the two random field kernels, and solid volume fraction of binder regions. The optimizer can adjust size parameters of the selected grain generator, but it will not automatically switch between sphere, ellipsoid, and convex polyhedron generators, nor between single‑ and dual‑random‑field models. These modeling types must be preselected by the user.

Global vs. Local Optimization

When UseManual is selected, user‑entered parameters serve as the starting point for local optimization. This approach is suitable when grain size is already known, experience with similar structures exists, or the parameter search range needs to be narrowed. When the Global Optimizer is selected, the GeoApp first searches for good initial parameters within a defined range using a differential evolution algorithm, then passes them to the local optimizer. Larger population sizes and global iteration counts generally explore the parameter space more thoroughly, but increase computation time. The Nelder–Mead Local Optimization is the GeoApp's main iterative optimization method. Each iteration involves generating a structure with current parameters, analyzing its properties, comparing with the reference, computing a scalar error, and updating the next set of parameters.

Independent Model Size and Resolution

The GeoApp allows users to create the final twin at different resolutions and volumes, independent of the structure size used in the optimization loop. This means users can use smaller models for parameter optimization, create larger 3D structures after obtaining optimal generation parameters, generate multiple different random realizations, change voxel size, conduct representative elementary volume studies, and build models of appropriate size for subsequent property simulations.

Anisotropy and Expert Settings

By default, grain orientations use an isotropic random distribution. Users can also define anisotropic grain orientation via an orientation tensor, giving ellipsoids or convex polyhedra a higher probability of aligning in specific directions. Expert settings also include inverting grain and pore phases, squaring the random field, inverting the squared random field, adjusting local optimization step size, controlling intermediate file retention, and specifying optimization model geometry dimensions.

Results and Reports

When optimization completes, GeoDict automatically opens the result file, which includes structure details (grid size, voxel length, and solid volume fraction of the reference structure, the twin used during optimization, and the final 3D digital twin), structure generation parameters (optimal parameters obtained from optimization, which can be reused to generate additional statistically equivalent twins), structure comparison (comparison of target metrics between reference and final twin, with corresponding errors), optimization record (global and local iteration counts, function evaluations, and total computation time), and plots (parameter changes over evaluations, error function convergence). The results folder may also contain analysis results of the reference structure and the final twin, intermediate candidate structures, CSV files of parameters and error function results at each step, and the final twin structure file (Structure.gdt).

Official Application Examples

Spherical Grain Packing – Using 2D segmented images from 3D CT scans as reference, matching pore size, grain size, chord length, and surface area.

Lithium‑ion Battery NMC Cathode – Using 2D segmented images from 3D FIB‑SEM data as reference, matching pore size, grain size, and surface area.

North Sea Sandstone – Using 2D SEM images as reference, after segmentation and cropping, matching pore size, grain size, chord length, and surface area, then generating the corresponding 3D digital rock model.

Sintered Titanium‑Based GDL for Fuel Cells – Using 2D slices from 3D CT scans as reference, generating a statistical digital twin of the sintered titanium‑based gas diffusion layer.

Typical Application Areas

The Generate Granular Twin GeoApp is suitable for materials with granular, sintered, or continuous random solid phase characteristics, including lithium‑ion battery anodes and cathodes, fuel cell porous transport layers, sintered metals, ceramic materials, digital rocks and reservoir rocks, powders and compacted materials, catalyst supports, porous electrodes, spherical or non‑spherical grain packings, and polymer concrete and other granular composites.

Required GeoDict Modules

According to Math2Market's official configuration, the core modules required are GrainGeo for grain, random field, overlay structure, and final 3D twin generation; PoroDict for pore size, porosimetry, and pore chord length analysis; MatDict for solid phase size, solid chord length, and specific surface area analysis; GeoApp‑2Dto3D when using 2D reference images to generate 3D twins; FlowDict when permeability is selected as a matching target; and DiffuDict when diffusivity is selected as a matching target. Commonly used supporting modules include ImportGeo‑Vol for 3D image import, processing, and segmentation; GrainFind for grain identification; FlowDict for flow and permeability prediction; and DiffuDict for diffusion and transport property prediction. The specific module combination depends on the reference data type and the target properties to be matched.