🔬 materials science

MOSAIC: Addressing Space for Local, Steerable, and Scalable Atomistic Generation

The paper introduces Mosaic, a hybrid mesh-particle representation that partitions space into anchored atom slots to enable local control, hierarchical generation, and scalable assembly of atomistic structures ranging from individual molecules to million-atom polycrystals.

Original authors: Ishan Nadkarni, Sebastien Hamel, Flynn Walsh, Fei Zhou

Published 2026-10-06

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CC BY 4.0

Original authors: Ishan Nadkarni, Sebastien Hamel, Flynn Walsh, Fei Zhou

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the quest to design new medicines and stronger materials, scientists have long relied on a fundamental truth: the properties of matter depend entirely on how its atoms are arranged. For decades, researchers could only study these arrangements after they were built, or simulate small, perfect crystals in a vacuum. Recently, a new wave of artificial intelligence has begun to generate these atomic structures from scratch, creating molecules that look chemically plausible. However, a major hurdle remains. Current AI models struggle to build large, complex structures while keeping precise control over specific parts. They are like architects who can design a single room perfectly but cannot assemble a skyscraper where a specific window must be placed in a specific spot without the whole building collapsing. This limitation has kept the most promising applications—such as designing drug molecules with a specific active site or engineering metal alloys with tailored internal boundaries—out of reach.

A team of researchers has now introduced a new way to organize this digital construction process, allowing for the generation of matter that is both massive and precisely controlled. Their method, called Mosaic, solves the problem by giving every potential atom a permanent address before it is even placed. Instead of asking an AI to figure out where every atom goes in a chaotic cloud, Mosaic divides the space into a grid of fixed locations, or "slots." Each slot acts as a designated parking spot that can either remain empty or hold an atom. If an atom is placed there, the system records exactly which slot it occupies and how far it has shifted from the center of that slot. This simple change transforms the generation process. By anchoring atoms to specific addresses, the AI can focus on filling one small neighborhood at a time, ensuring that the local chemistry makes sense without losing track of the overall structure.

The researchers tested this approach on two very different scales. First, they applied it to the creation of drug-like molecules. In these tests, the system was asked to build molecules containing up to 120 atoms. Without the new method, similar AI models often produced broken structures where atoms were disconnected or chemically impossible. With Mosaic, the success rate for creating valid, connected molecules remained high even as the size increased. More importantly, the researchers could issue specific instructions, such as "place a chemical group here," and the system would reliably generate that feature in the correct location while maintaining the integrity of the rest of the molecule. The system achieved this by treating the generation of the molecule's skeleton and the placement of its atoms as a coordinated, step-by-step process, rather than a single chaotic leap.

The true power of this method, however, was revealed when the team scaled it up to the size of real-world materials. They used Mosaic to generate polycrystals of nickel, a material used in everything from jet engines to battery electrodes. These are not small, perfect crystals but complex assemblies of millions of atoms with different internal orientations, known as grains. The researchers provided the AI with a coarse map describing the desired shape and arrangement of these grains. The system then built the structure block by block, using the generated boundary of one block to inform the next. The result was a digital nickel crystal containing more than 1.1 million atoms, a scale that previous methods could not handle with such structural coherence. The generated material faithfully reproduced the complex grain boundaries and internal order required for real engineering applications.

This work demonstrates that by changing how space is represented in a computer, scientists can overcome the size limits that have held back generative design. The method does not rely on a specific type of neural network but can be paired with various existing AI backbones, making it a flexible tool for future discovery. The researchers showed that by giving atoms a fixed address, they could steer the generation of matter with a level of precision that was previously impossible, from the tiny scale of a single drug molecule to the massive scale of a million-atom metal structure. This approach suggests a future where engineers can design materials with custom internal architectures, tailoring strength and flexibility to exact specifications, simply by defining the map of where the atoms should go.

Technical Summary: MOSAIC – Addressing Space for Local, Steerable, and Scalable Atomistic Generation

1. Problem Statement

Generative models have demonstrated success in creating chemically plausible molecules and candidate periodic crystals. However, for engineering applications, a critical gap remains: the ability to specify what should change, where it should change, and what surrounding structure must be preserved. Current methods struggle with:

Local Control: Tasks such as replacing a chemical group while retaining a molecular framework, redesigning specific protein segments, or modifying material interfaces require generation that is consistent with the local atomic environment.
Scalability: Existing approaches often fail to scale beyond isolated molecules or small periodic cells to large, heterogeneous structures (e.g., polycrystals with millions of atoms) while maintaining structural coherence.
Representation Limitations: Unordered particle sets lack persistent spatial addresses for selected regions (including empty ones), while grid-based methods represent atoms indirectly, requiring particle recovery after generation.

2. Methodology: The Mosaic Representation

The paper introduces Mosaic, a hybrid mesh–particle representation designed to partition space into anchored regions containing "atom slots." This representation is distinct from a specific generative model; rather, it provides a spatial interface that can be paired with various generative backbones (e.g., diffusion or flow matching).

2.1 Core Representation

Spatial Anchors: The domain $\Omega$ is partitioned into regions $\{C_v\}$ , each associated with a fixed anchor point $R_v$ (using SC, BCC, or FCC grids).
Atom Slots: Each region contains $K_v$ $K_{v}$ local slots. A slot $s_{vk}$ $s_{v k}$ stores:
- Occupancy/Species ( $a_{vk}$ ): An atomic species or a physical empty state $X$ .
- Displacement ( $\delta_{vk}$ ): A continuous vector representing the atom's position relative to the anchor ( $r_i = R_v + \delta_{vk}$ ).
Decoding: Occupied slots decode directly to continuous particles. The mesh discretizes spatial ownership but does not quantize final coordinates. Unused slots in fixed-capacity settings take the empty state $X$ .

2.2 Generative Modeling

The generative process factors into slot support prediction and atom generation:
$p(S | c) = p_\phi(O | c) \, p_\theta(A, \Delta | O, c)$
where $O$ is the slot support, and $(A, \Delta)$ are species and displacements.

A. Molecular Generation (Hierarchy and Steering)

Stage 1 (Support): A spatial Diffusion Transformer (CountDiT) refines a sparse hierarchy of cell counts to define the support. It uses an absorbing masked diffusion process to predict local atom counts $n_v$ at the finest level, ensuring the total count matches the request $N^\star$ .
Stage 2 (Generation): An equivariant flow matching model generates atomic species and continuous coordinates on the fixed support defined by Stage 1.
Steering: Spatial prompts (chemical groups and centers) guide both stages via classifier-free guidance, allowing users to specify where functional groups should appear.

B. Polycrystal Generation (Morphology and Scale)

Mesoscale Conditioning: Grain morphology is prescribed via a map $M(x)$ defining grain fractions. Reciprocal-space features (vectors $q$ and complex coefficients) encode lattice orientation and phase, ensuring crystal registry.
Bounded Autoregressive Assembly: The model operates on bounded blocks (e.g., 16 Å). An outer autoregressive traversal generates blocks in raster order, conditioning each new block on:
1. Prescribed morphology and reciprocal fields.
2. Generated boundary atoms from previously completed blocks (within a 6 Å radius).
Scalability: Because each step processes only a bounded block and its immediate predecessor context, memory usage does not scale with the total system size, enabling the generation of structures with >1 million atoms.

3. Key Contributions

Data Representation: A hybrid mesh–particle representation combining continuous coordinates with persistent spatial addresses, enabling local conditioning across diverse generative backbones.
Empirical and Theoretical Support:
- Ablations: Matched-backbone experiments show that local support and coordinate priors significantly improve molecular connectivity and validity compared to global-center approaches.
- Theoretical Bounds: Analysis shows that per-particle transport action is bounded by the cell width $h^2$ (independent of system size) and that spatial addressing reduces permutation ambiguity from $O(N \log N)$ to $O(N \log K)$ .
Control and Assembly: Demonstrated ability to steer molecular functional groups and generate atomistic polycrystals with prescribed grain morphology and orientation, scaling to over one million atoms.

4. Results

4.1 Molecular Generation

Quality: On the QM9 dataset, Mosaic achieved 84.44% strict all-request validity. On GEOM-Drugs, it more than doubled the connected-valid rate of the released EDM model (77.2% vs. 34.9%) and outperformed it in sampling efficiency (3.07× throughput of MegalodonFlow in connected-valid molecules per second).
Scaling: As molecule size increased (30–120 atoms), Mosaic maintained high connectivity (26% at 120 atoms), whereas EDM dropped to 0%.
Control: Spatial prompts successfully steered the placement of amide, ester, and aromatic groups while preserving requested atom counts.

4.2 Polycrystal Generation

Local Control: Reciprocal-phase conditioning reduced structural errors (PTM, RDF, bond angles) by 5.2–35× compared to models without such features.
Morphology: The model successfully generated bicrystals, tricrystal junctions, and eight-grain Voronoi polycrystals matching prescribed coarse maps.
Scale: The system generated three nickel polycrystals containing 1.09–1.12 million atoms from coarse morphology maps, maintaining local crystallinity and coherent assembly across extended domains.

5. Significance and Claims

The paper posits that local spatial addressing is a practical foundation for the steerable generation of matter across scales. By decoupling the representation from the generative backbone, Mosaic allows existing equivariant and Transformer pipelines to be enhanced with local control and scalable assembly capabilities.

From Molecules to Materials: The approach bridges the gap between isolated molecule generation and large-scale material engineering, enabling tasks like defect introduction and interface modification.
Efficiency: The bounded autoregressive assembly turns large-scale generation into a manageable problem where memory and computation per step remain constant, regardless of the total number of atoms.
Future Potential: The authors suggest this hierarchy could extend to larger biomolecules and proteins, and that mesh fields could encode additional physical properties (charge, stress, density) from experiments or continuum simulations.

The work establishes that by making locality part of the particle representation, generative models can achieve both fine-grained spatial control and the scalability required for engineering-relevant structures.